Natalia Dilna, PhD

	Mgr. Natalia Dilna, PhD.
	Scientific degree: PhD Place of birth: Ternopil, Ukraine Mailing address: Mathematical Institute Slovak Academy of Sciences Stefanikova 49 Str. Bratislava 81473 Slovak Republic E-mail: natalia.dilna(at)mat.savba.sk Tel: +421 2 57510409 Fax: +421 2 52497316
Curriculum Vitae About me I was born in the city of Ternopil in the Western Ukraine. In 2001 I obtained Master's Degree from the Physical-Mathematical Faculty of the Ternopil State Pedagogical University. Afterwards, in 2001, I started my postgraduate studies in the Institute of Mathematics of the National Academy of Sciences of Ukraine and, in 2006, defended my PhD Thesis entitled Solvability of the initial-value problems for positive systems of functional-differential equations and prepared under the supervision of Academician, Prof., DrSc. Anatoly Samoilenko and Prof., DrSc. András Rontó. In 2004, I had become a researcher at the Institute of Mathematics of the National Academy of Sciences of Ukraine. Now I am a Research Fellow in the Mathematical Institute of the Slovak Academy of Sciences. Education 1996-2001: Ternopil State Pedagogical University, Ternopil, Ukraine (graduate student) 2001-2004: Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine (PhD student) Work 2004-2008: Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine (Junior Research Fellow) 2008-2010: Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine (Research Fellow) Since 2009: Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia (Research Fellow) Awards 2. place at the Competition for Young Scientists SAS till 35 years (Bratislava, Slovak Republic, 2011) Honorable Mention 2009 at the Slovak Contest for Young Scientist of the Year 2009 (Bratislava, Slovak Republic) for a series of works on differential equations Project participation 2024-2027: VEGA 2/00062/24 Qualitative properties and oscillations of differential equations and dynamical systems 2020-2023: VEGA 2/0127/20 Qualitative properties and bifurcations of differential equations and dynamical systems 2016-2019: VEGA 2/0153/16 Qualitative properties and bifurcations of differential equations and dynamical systems 2018-2020: ITSM2014+ - NFP313011T634 (Výskum v oblasti analýzy heterogénnych dát za úèelom predikcie zmeny zdravotného stavu chronických pacientov/Research in the field of heterogeneous data analysis to predict changes in the health status of chronic patients) 2018-2020: ITSM2014+ - NFP313011T683 (Matematická podpora kvantových technológií/Mathematical support for quantum technologies) 2013-2015: VEGA 2/0029/13 Qualitative properties and bifurcations of differential equations and dynamical systems 2011-2014: APVV-0134-10 Nonlinear phenomena in continuous and discrete dynamical systems 2010-2012: VEGA 2/0124/10 Qualitative property and bifurcation of the differential equations and dynamical systems 05.2009-03.2012: Stipendium of the Fond of Stefan Schwartz 2009: VEGA 2/7140/27 Qualitative property and bifurcation of the differential equations and dynamical systems 07.2008-12.2008: Grant No. GP/F26/0154 of the Fundamental Researches State Fund of Ukraine 03.2008-12.2008: Grant No. 0108U004117 of the Presidium of National Academy of Sciences of Ukraine for young researchers 2007: Grant No. 0107U003322 of the Fundamental Researches State Fund of Ukraine 2005-2006: Grant No. 0105U005666 of the Presidium of National Academy of Sciences of Ukraine for young researchers Attended research stays 09.2008-02.2009: National Scholarship Programme of Slovak Republic. Mathematical Institute, Slovak Academy of Sciences, Bratislava 02.2008-06.2008: National Scholarship Programme of Slovak Republic. Mathematical Institute, Slovak Academy of Sciences, Bratislava 25.09.2003-04.10.2003: Institute of Mathematics, Czech Academy of Sciences, Brno Research interests Boundary-value problems for the functional and ordinary differential equations; Periodic solutions of the functional and symmetric functional and ordinary differential equations; Existence of solutions of the functional differential equations and fractional functional differential equations; Conditions on a unique solvability of the functional and symmetric ordinary differential equations; Boundary-value problems for the functional differential equations of the fractional order; Theory of stability. Reviewing activities A reviewer for Zentralblatt fur Mathematik Talks at the scientific seminars Mathematical seminar "Aka si mi krasna", Matej Bel University (Banska Bystrica, Slovak Republic, 19.05.2009) Seminar on Differential Equations and Dynamical Systems, Faculty of Natural Sciences, Comenius University (Bratislava, Slovak Republic, 27.02.2009) Seminar on the Difference and Differential Equations, University of Zilina (Zilina, Slovak Republic, 09.06.2008) Seminar on the Quantum Logics, Centre of Excellence of the Slovak Academy of Sciences CE PI, Mathematical Institute of the Slovak Academy of Sciences (Bratislava, Slovak Republic, 29.02.2008) Seminar on the Department of Differential Equations and Nonlinear Oscillations, Institute of Mathematics, National Academy of Sciences of Ukraine (Kiev, Ukraine, 12.11.2007) Seminar on the Department of Differential Equations and Nonlinear Oscillations, Institute of Mathematics, National Academy of Sciences of Ukraine (Kiev, Ukraine, 25.10.2005) Seminar on the Department of Differential Equations and Nonlinear Oscillations, Institute of Mathematics, National Academy of Sciences of Ukraine (Kiev, Ukraine, 20.09.2004) Seminar on Qualitative Theory of Ordinary and Functional Differential Equations, Institute of Mathematics, Academy of Sciences of the Czech Republic (Brno, Czech Republic, 01.10.2003) Talks on scientific conferences ICFDA 2024 Conference on Fractional Differentiation and its Applications (Bordeaux, France, 9.07-12.07.2024) The Equadiff conference 2024 (Karlstad, Sweden, 10.06-14.06.2024) The 34th International Workshop on Operator Theory and is Applications (IWOTA 2023) (Helsinki, Finland, 31.7- 4.8.2023) New Trends in the Applications of Differential Equations in Sciences (NTADES’23) (St. Constantine and Helena, Bulgaria, 17-20.7.2023) Equadiff 15, Conference on Differential Equations and Their Applications (Brno, Czech Republic, 11–15.07.2022) International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22, Instituto superior de engenharia do Porto, (Porto, Portugal, 27-29.07.2022) International Conference on Differential and Difference Equations and Applications 2019 (ICDDEA 2019) (Lisbon, 1-5.07.2019) Research Workshop of Israel Science Foundation Functional Differential Equations and Applications (FDE 2010) (Ariel, Israel, 27.08-04.09.2010) 8 th AIMS International Conference on Dynamical Systems, Differential Equations and Applications (Dresden, Germany, May 25 - 28, 2010) Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine (Santiago de Compostela, Spain, 16-19.09.2008) International Conference on the Occasion of the 150th Birthday of A. M. Lyapunov "Lyapunov Memorial Conference" (Kharkiv, Ukraine, 24 - 30.06.2007) The 12th International Conference "Mathematical Modelling and Analysis" (Trakai, Lithuania, 30.05 - 2.06.2007) The 8th International Crimean mathematical school "Method of Lyapunov Functions and Its Applications" (Crimea, Alushta, 11 - 17.09.2006) Conference on Differential and Difference Equations (Brno, Czech Republic, 5 - 8.09.2006) Workshop-2006 "Constructive Methods in Nonlinear Boundary Value Problems" (Sarospatak, Hungary, 7-10.06.2006) The 11th International Scientific Conference dedicated to memory of academician M. M. Kravchuk (Kyiv, National Technical University of Ukraine, 18 - 21.05.2006) XI Konferencija "Matematyka w naukah technicznych i przyrodniczych" (Krynica, Poland, 30.09.2005 - 03.10.2005) International conference "Integral Equations and Their Applications" (Odesa, Ukraine, 29.06 -4.07.2005) International conference "Differential Equations and Their Applications" (Kyiv, Ukraine, 6.06 - 12.06.2005) Young scientists conference "Actual Problems of Mechanics and Mathematics - 2005" dedicated to memory of academician Ya. S. Pidstryhach (Lviv, Ukraine, 24 - 27.05.2005) VIII Konferencija "Matematyka w naukah technicznych i przyrodniczych" (Krynica, Poland, 30.09.2004- 03.10.2004) The 7th International Crimean mathematical school "Method of Lyapunov Functions and Its Applications" (Crimea, Alushta, 11 - 18.09.2004) The 10th International Scientific Conference Dedicated to the Memory of Academician M. M. Kravchuk (Kyiv, National Technical University of Ukraine, 13 - 15.05.2004) VIth International Scientific Conference Dedicated to the Memory of M. M. Bogoliubov (Chernovtsy, Ukraine, 26 - 30.08.2003) The 7th Colloquium on the Qualitative Theory of Differential Equations (Szeged, Hungary, Bolyai Institute, University of Szeged, 14 - 18.07.2003) International Mathematical Conference on Differential Equations and Applications (Zilina, Slovakia, 30.06.2003 - 04.07.2003) International Scientific Conference on Modelling and Investigation of Stability of Systems (Kyiv, Ukraine, 27- 30.05.2003) Language skills Ukrainian, Russian, English, Slovak ORCID PUBLONS SCOPUS GoogleScholar List of publications LIST OF PUBLICATIONS N. Dilna, G. Fekete, M. Langerová, B. Tóth. Ulam–Hyers and Generalized Ulam–Hyers Stability of Fractional Differential Equations with Deviating Arguments. Mathematics 2024, 12, 3418. https://doi.org/10.3390/math12213418 N. Dilna, M. Langerova. Ulam-Hyers and generalized Ulam-Hyers stability of fractional functional integro-differential equations, IFAC PapersOnLine, 58-12 (2024) 280–285, Vol. 278, No. 6, (2024) https://doi.org/10.1016/j.ifacol.2024.08.203 S. Leshchuk, N. Dilna, I. Grod, O. Radchenko, T. Hnoiova. The implementation of STE(A)M education through Scratch projects, Journal of Physics: Conference Series, 2871 (2024) 012018 https://doi.org/10.1088/1742-6596/2871/1/012018 X. Jiang, I. Bíró, H.-Q. Wang, N. Dilna, K. Nemoga, G. Fekete. Experimental Study on Ground Reaction Force Parameters with Regard to Novice and Recreational Runners. Advances in Transdisciplinary Engineering, Material Strength and Applied Mechanics, V. 59 (2024) pp. 530-537 https://doi.org/10.3233/ATDE240590 G. Fekete, M. Máté, I. Popa-Muller, H-Q. Wang, N. Dilna, K. Nemoga. Computational Wear Prediction in Total Knee Replacements as a Function of Replacement Size. Series Advances in Transdisciplinary Engineering, V. 59: Material Strength and Applied Mechanics. 494-500 (2024) https://doi.org/10.3233/ATDE240585 N. Dilna, M. Feèkan, JR. Wang. Note on quaternion linear dynamical systems, Journal of Mathematical Sciences, Vol. 278, No. 6, (2024) https://doi.org/10.1007/s10958-024-06973-w N. Dilna. Precise conditions on the unique solvability of the linear fractional functional differential equations related to the Sigma-nonpositive operators. Fractal Fract. 2023, 7(10), 720. https://doi.org/10.3390/fractalfract7100720 N. Dilna, M. Feèkan, A. Rontó. Solvability of the symmetric nonlinear functional differential equations, Mathematical Methods in the Applied Sciences, V. 46, No.18 (2023), pp.18975-18984, https://doi.org/10.1002/mma.9603 N. Dilna. General exact solvability conditions for the initial value problems for linear fractional functional differential equations, Archivum Mathematicum, Vol. 59, No.1 (2023), pp.11–19 https://doi.org/10.5817/AM2023-1-11 N. Dilna, S. Leshchuk. D-stability of the model of the Stieltjes string, Applicable Analysis, V. 102, No. 18, pp. 5157–5169 (2023), 100092 https://doi.org/10.1080/00036811.2023.2168654 N. Dilna. Unique solvability of the initial-value problem for fractional functional differential equations—Pantograph-type model. Fractal Fract. 2023, 7, 65. https://doi.org/10.3390/fractalfract7010065 N. Dilna. D-stability of the model of the Stieltjes string related to the functional differential equations, Examples and Counterexamples, V. 2 (2022), 100092 https://doi.org/10.1016/j.exco.2022.100092 N. Dilna, M. Feèkan. Exact solvability conditions for the non-local initial value problem for systems of linear fractional functional differential equations. Mathematics, 10 (10), 1759, (2022) https://doi.org/10.3390/math10101759 N. Z. Dilna, M. I. Gromyak, S. Leshchuk. Unique solvability of the boundary value problems for nonlinear fractional functional differential equations. Journal of Mathematical Sciences. V. 265, (4), 2022 p. 577-588 https://doi.org/10.1007/s10958-022-06072-8 N. Dilna, A. Dvurecenskij. Prof. RNDr. Michal Feckan, DrSc. – Sexagenarian?, Math. Slovaca 71 (2021), 265-266 https://doi.org/10.1515/ms-2017-0465 N. Z. Dilna, A. Dvurecenskij. Michal Feckan (on his 60th birthday). Nonlinear Oscillations V. 24, No 1. 2021, pp. 141-144 https://www.imath.kiev.ua/~nosc/admin/private/published_files/1335/NOSC13352021241998.pdf N. Dilna. On Non-local Boundary-Value Problems for Higher-Order Non-linear Functional Differential Equations. In: Pinelas S., Graef J.R., Hilger S., Kloeden P., Schinas C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, (2020) vol 333. pp. 535-548 Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_40 N. Dilna, M. Feèkan and M. Solovyov. D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations, Symmetry (2020), 12(11), 1761; https://doi.org/10.3390/sym12111761 N. Dilna, M. Feèkan and A. Rontó. On a class of functional differential equations with symmetries, Symmetry (2019), 11, 1456. https://doi.org/10.3390/sym11121456 N. Dilna, M. Feckan, M. Solovyov and JR. Wang. Symmetric nonlinear functional differential equations at resonance, Electron. J. Qual. Theory Differ. Equ. No. 76 (2019), 1-16. https://doi.org/10.14232/ejqtde.2019.1.76 N. Dilna and M. Feckan. The Stieltjes string model with external load. Applied Mathematics and Computation, Vol. 337 (2018), p. 350-359. https://doi.org/10.1016/j.amc.2018.05.026 N. Dilna. On the unique solvability of a nonlinear nonlocal boundary-value problem for systems of second-order functional differential equations. Journal of Mathematical Sciences, Vol. 223 (June, 2017) No. 3, pp. 257-272. https://doi.org/10.1007/s10958-017-3352-1 M. Feckan , A. Ronto, N. Dilna. On a kind of symmetric weakly non-linear ordinary differential systems. Bulletin des sciences mathématiques, vol. 140, no. 2, (2016), pp. 188-230. https://doi.org/10.1016/j.bulsci.2015.11.003 N. Dilna. Unique solvability of second order functional differential equations with non-local boundary conditions. E. J. Qualitative Theory of Diff. Equ., No. 14 (2012), pp. 1-13. https://doi.org/10.14232/ejqtde.2012.1.14 N. Dilna and M. Feckan.On symmetric and periodic solutions of parametric weakly nonlinear ODE with time-reversal symmetries. Bulletin of the Belgian Mathematical Society - Simon Stevin, Vol. 18, No. 5 (2011), pp. 896-923. https://doi.org/10.36045/bbms/1323787175 N. Dilna. About symmetric solutions of a class of functional differential equations. Reports of the National Academy of Sciences of Ukraine, No. 9 (2011), pp.7-10. N. Dilna and A. Ronto. Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations. Mathematica Slovaca, Vol. 60 (2010), No. 3., pp. 327–338. https://doi.org/10.2478/s12175-010-0015-9 N. Dilna and M. Feckan. On the uniqueness, stability and hyperbolicity of symmetric and periodic solutions of weaker nonlinear ordinary differential equations. Miskolc Mathematical Notes, Vol. 10 (2009), No. 1, pp. 11-40. https://doi.org/10.18514/MMN.209.200 N. Dilna and M. Feckan. About the uniqueness, stability and hyperbolicity of symmetric and periodic solutions of weaker nonlinear ordinary differential equations. Reports of the National Academy of Sciences of Ukraine, (2009), No. 5, pp. 22-28 (in Russian). N. Dilna and M. Feckan. Weakly non-linear and symmetric periodic systems at resonance. Journal Nonlinear Studies, Vol. 16 (2009), No. 2, pp. 23-44. N. Dilna and A. Ronto. General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations. Mathematica Bohemica. Vol. 133 (2008), No. 4, pp. 435-445. https://mb.math.cas.cz/full/133/4/mb133_4_9.pdf Nataliya Dilna. On Unique Solvability of the Initial Value Problem for Nonlinear Functional Differential Equations. Memoirs on Differential Equations and Mathematical Physics. Vol. 44 (2008), pp. 45-57. https://www.emis.de/journals/MDEMP/vol44/vol44-3.pdf http://www.jeomj.rmi.acnet.ge/memoirs/vol44/contents.htm N. Z. Dilna and A. N. Ronto, V. A. Pylypenko. Some conditions for the unique solvability of a nonlocal boundary-value problem for linear functional differential equations. Reports of the National Academy of Sciences of Ukraine, (2008), No. 6, pp. 13- 18 (in Ukrainian). A. Ronto, V. Pylypenko and N. Dilna. On the unique solvability of a non-local boundary value problem for linear functional differential equations. Mathematical Modelling and Analysis. Vol. 13 (2008), No. 2, pp. 241-250. https://doi.org/10.3846/1392-6292.2008.13.241-250 N. Z. Dilna and A. N. Ronto. General conditions for the unique solvability of initial-value problem for nonlinear functional differential equations. Ukrainian Mathematical Journal. Vol. 60 (2008), No. 2, pp. 167-172. https://doi.org/10.1007/s11253-008-0051-6 A. N. Ronto and N. Z. Dilna. Conditions for the unique solvability of the initial-value problem for linear second-order differential equations with argument deviations. Nonlinear Oscillations. Vol. 9 (2006), No. 4, pp. 535-547. https://doi.org/10.1007/s11072-006-0059-5 A. M. Samoilenko, N. Z. Dilna, and A. N. Ronto. Solvability of the Cauchy problem for linear integral-differential equations with transformed arguments. Nonlinear Oscillations. Vol. 8 (2005), No. 3, pp. 388-403. https://doi.org/10.1007/s11072-006-0008-3 N. Dilna. On the solvability of the Cauchy problem for linear integral differential equations, Miskolc Mathematical Notes. Vol. 5 (2004), No. 2, pp. 161- 171. http://mat76.mat.uni-miskolc.hu/~mnotes/contents.php?volume=5&number=2#article104 N. Z. Dilna and A. N. Ronto. On the solvability of the Cauchy problem for systems of linear functional differential equations with (\sigma, \tau)-positive right-hand sides. Reports of the National Academy of Sciences of Ukraine. (2004), No. 2, pp. 29- 35 (in Russian). N. Z. Dilna and A. N. Ronto. Some new conditions for the solvability of the Cauchy problem for systems of linear functional-differential equations. Ukrainian Mathematical Journal. Vol. 56 (2004), No. 7, pp. 867 - 884. https://doi.org/10.1007/PL00022171 N. Dilnaya and A. Ronto. Multistage iterations and solvability of linear Cauchy problems, Miskolc Mathematical Notes. Vol. 4 (2003), No. 2, pp. 89-102. http://mat76.mat.uni-miskolc.hu/~mnotes/contents.php?volume=4&number=2#article81 PREPRINTS Nataliya Dilna, Michal Feckan. On the uniqueness and stability of symmetric and periodic solutions of weakly nonlinear ordinary differential equations. Preprint of the Mathematical Institute of the Slovak Academy of Sciences, Bratislava. 3/2008 (July 8, 2008), 30 p. http://www.mat.savba.sk/preprints/2008.htm Nataliya Dilna, Michal Feckan. Weakly nonlinear and symmetric periodic systems at resonance. Preprint of the Mathematical Institute of the Slovak Academy of Sciences, Bratislava. 1/2009 (February 9, 2009), 21 p. http://www.mat.savba.sk/preprints/2009.htm LIST OF ABSTRACTS N. Dilna, M. Langerova. Ulam-Hyers and Generalized Ulam-Hyers Stability of Fractional Functional Integro-Differential Equations,ICFDA 2024 Conference on Fractional Differentiation and its Applications (Bordeaux, France, 9.07-12.07.2024) https://ifac.papercept.net/conferences/scripts/rtf/FDA24_ContentListWeb_3.html N. Dilna. D-stability of the model of the Stieltjes string. Equadiff 2024, Karlstad, Sweden, 10-14 June, 2024, https://www.kau.se/files/2024-06/Book_of_Abstracts%28a%29.pdf p.280 N. Dilna. General Exact Solvability Conditions for the Initial Value Problems for Linear Fractional Functional Differential Equations. The 34th International Workshop on Operator Theory and is Applications (IWOTA 2023), 31.7- 4.8. 2023, https://www.helsinki.fi/assets/drupal/2023-08/IWOTA_2023_update_v4_0.pdf p. 69 N. Dilna. Exact Conditions on the Unique Solvability of the Linear Fractional Functional Differential Equations. New Trends in the Applications of Differential Equations in Sciences (NTADES’23) 17-20 July, 2023, St. Constantine and Helena, Bulgaria http://www.ntades.eu/ N. Dilna. D-stability of the initial value problem for symmetric nonlinear functional differential equations. Equadiff 15, Conference on Differential Equations and Their Applications (Brno, Czech Republic, 11–15.07.2022), https://conference.math.muni.cz/equadiff15/files/book-of-abstracts.pdf p.157 N. Dilna. Exact solvability conditions for the model with a discrete memory~effect. International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts, ISBN 978-989-53496-3-0, (2022), pp. 405-407 https://doi.org/10.34630/20734 , International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22, Instituto superior de engenharia do Porto, (Porto, Portugal, 27-29.07.2022) M. Feckan, A. Ronto, N. Dilna. On the existence and stability of symmetric solutions in a class of weakly non-linear systems. 3rd International Conference on Pure and Applied Mathematics. Van Yuzuncu Yil University, Van, TURKEY, (Van, Turkey, September 3-5, 2020) http://http://icpam.yyu.edu.tr/abstractbook_isbn.pdf p.23 N. Dilna, M. Feckan, M. Solovyov and JR. Wang. Symmetric nonlinear functional differential equations at resonance. International Conference on Differential and Difference Equations and Applications (Lisbon, Portugal, 1-5.07.2019) https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxzYW5kcmFwaW5lbGFzfGd4OjNmMGFkOTAzNjE3ZTQwYmI p.132 N. Dilna and M. Feckan. About parametric weakly nonlinear ODE with time-reversal symmetries. International Conference "Painleve Equations and Related Topics" (St.Petersburg, Russia, 17-23.06.2011) http://www.pdmi.ras.ru/EIMI/2011/PC/proceedings.pdf - p. 46-49. N. Dilna and M. Feckan. On parametric weakly nonlinear ODE with time-reversal symmetries. International Scientific Conference "Differential equations and their applications" (Kiev, Ukraine, 8-10.06.2011) -p. 167. N. Dilna and A. Ronto. About the unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional-differential equations. Research Workshop of Israel Science Foundation Functional Differential Equations and Applications (FDE 2010) (Ariel, Israel, 27.08-04.09.2010) http://www.ariel.ac.il/projects/math/adom/abs.pdf N. Z. Dilna. Unique Solvability of the Initial Value Problem for Nonlinear Functional Differential Equations. Mathematics and life sciences: possibilities, interlacements and limits (Kyiv, Ukraine, 05-08.08.2010) http://hk2010.rivok.com//abstracts/pdf/162.pdf N. Dilna and M. Feckan. Weakly Nonlinear and Symmetric Periodic Differential Systems // 8th AIMS International Conference on Dynamical Systems, Differential Equations and Applications (Dresden, Germany, May 25 - 28, 2010) P. 41 http://www.math.tu-dresden.de/aims2010/abstracts/ss7-4.pdf N. Dilna and M. Feckan. On the weakly nonlinear and symmetric periodic systems at resonance // International Conference - Ukrainian Mathematical Congress - 2009. Dedicated to the Centennial of Nikolai N. Bogoliubov. (Kyiv, Institute of Mathematics of NASU, 27-29.08.2009) http://www.imath.kiev.ua/~congress2009/Abstracts/DilnaFeckan.pdf N. Dilna and M. Feckan. About the uniqueness and stability of symmetric and periodic solutions of weakly nonlinear ordinary differential equations // International Conference dedicated to the 100-th anniversary of M. M. Bogolyubov and to the 70-th anniversary of M.I. Nahnybida (Chernivtci, Ukraine, 8-13.06.2009) P. 230-231. N. Dilna and M. Feckan. The stability of a unique symmetric and periodic solution of the ordinary differential equation //Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine (Santiago de Compostela, Spain, 16-19.09.2008) - P. 62. N. Dilna and A. Ronto. The unique solvability of the initial-value problem for non-linear functional differential equations // Conference on Differential and Difference Equations and Applications (Strecno, Slovakia, 23 - 27.06.2008) - P.18. N. Dilna and A.Ronto. About the unique solvability of the initial-value problem for non-linear functional-differential equations //International Scientific Conference dedicated to the birthday of Academician A. M. Samoilenko (Melitopol, Ukraine, 16 - 21.06.2008) - P. 45 N. Dilna and A. Ronto. Some conditions for unique solvability of the initial-value problem for linear second order functional-differential equations // International Conference on the occasion of the 150th birthday of A.M.Lyapunov "Lyapunov Memorial Conference" (Kharkov, Ukraine, 24 - 30.06.2007) - Karazin Kharkiv National University. - P. 33-34. N. Dilna and A. Ronto. On unique solvability of the initial-value problem for a second order FDE// The 12th International Conference "Mathematical modelling and analysis" (Trakai, Lithuania, 30.05 - 2.06.2007) - Vilnius Gedeminas Technical University. - P. 33. N. Dilna and A. Ronto. The 8th International Crimean Mathematical School Method of Lyapunov functions and it's application (Crimea, Alushta (Ukraine) 11- 17.09.2006) N. Dilna and A. Ronto. On the unique solvability of the Cauchy problem for linear Integral-differential equations with transformed argument // Conference on Differential and Difference Equations (Brno, Czech Republic, 5 - 8.09.2006) N. Dilna and A. Ronto. On the Cauchy problem for Linear Integral-Differential Equations with Argument Deviations // Conference on Differential and Difference Equations and Applications (Rajecke Teplice, Slovakia, 26 - 30.06.2006). - P. 17 - 18. N. Z. Dilna and A. M. Ronto. // The 11th International Scientific Conference dedicated to memory of academician M. M. Kravchuk (Kyiv, National Technical University of Ukraine, 17 - 21.05.2006) - National Technical University. - P. 126. N. Z. Dilnaya and A. N. Ronto. New conditions of solvability of the Cauchy problem for linear scalar differential equations with argument deviations // International conference "Integral Equations and Their Applications" (Odesa, Ukraine, 29.06 - 4.07.2005). - Odessa National University. - P. 48. N. Z. Dilna and A. M. Ronto. Solvability of the linear Cauchy problem for integral differential equations with (\sigma,\tau)-positive right-sides // International conference "Differential Equations and Their Applications" (Kyiv, Ukraine, 6 - 12.06.2005). - Kyiv National Shevchenko University - P. 27. N. Z. Dilna. Conditions of unique solvability of the Cauchy problem for linear integral-differential equations with (\sigma,\tau)-positive right-sides // Young scientists' conference "Modern Problems of Mechanics and Mathematics - 2005" dedicated to the memory of Academician Ya. S. Pidstryhach (Lviv, Ukraine, (24 -27.05.2005). - Institute of Applied Problems of Mechanics and Mathematics, NAS of Ukraine. - P. 280. N. Z. Dilnaya and A. N. Ronto. Conditions of unique solvability of the linear Cauchy problem // The 7th International Crimean mathematical school "Method of Lyapunov Functions and Its Applications". - Alushta, Crimea: Tavric National University of Ukraine (11 - 18.09.2004). - P. 56. N. Dilna. Some theorems on the multistage iterations and solvability of linear Cauchy problem // International Conference "Analysis and its applications" (Mersin, Turkey, 07 - 11.09.2004). - Mersin University. -P. 26. N. Z. Dilna, A. M. Ronto. Multistage iterations and solvability of linear Cauchy problem // The 10th International Scientific Conference dedicated to memory of academician M. M. Kravchuk (Kyiv, National Technical University of Ukraine, 13 - 15.05.2004). - P. 100. N. Z. Dilna, A. M. Ronto. Some solvability conditions of the Cauchy problem for linear functional differential equations // Ukrainian scientific conference "Nonlinear Problems in Analysis" (Ivano-Frankivsk University named after Vasyl Stefanyk, (09 -12.09.2003). - P. 31. N. Z. Dilna, A. M. Ronto. About optimal conditions of the solvability Cauchy problem for functional differential equations // VI International Scientific Conference dedicated to the memory of M. M. Bogoliubov (Chernivtsi, Ukraine, 26 - 30.08.2003). - P. 61. A. Ronto, N. Z. Dilna. On the Cauchy problem for a class of linear functional differential equations // The 7th Colloquium on the Qualitative Theory of Differential Equations (Szeged, Hungary: Bolyai Institute, University of Szeged, 14 - 18.07.2003). -P. 40. N. Z. Dilna, A. N. Ronto. Some theorems on the Cauchy problem for linear functional differential equations // International Mathematical Conference on Differential Equations and Applications (Zilina, Slovakia, 30.06.2003 - 04.07.2003). - P. 14. N. Z. Dilnaya, A. N. Ronto. About unique solvability of the Cauchy problem for linear functional differential equations with (\sigma, tau)-positive right side. // International Scientific Conference on Modelling and Investigation of Stability of Systems (Kiev, Ukraine, 27- 30.05.2003).-P. 49. Research interests Boundary-value problems for the functional and ordinary differential equations; Periodic solutions of the functional and symmetric ordinary differential equations; Conditions on a unique solvability of the functional and symmetric ordinary differential equations; Boundary-value problems for the functional differential equations of the fractional order; Theory of stability; Application. Stieltjes string; Quaternion linear dynamical systems.