Curriculum Vitae
About me
I was born in the city of Ternopol in the Western Ukraine. In 2001 I obtained Master's Degree from the
PhysicalMathematical 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 initialvalue problems for positive systems of functionaldifferential equations
and prepared under the supervision of Academician, Prof.,DrSc. Anatoly Samoilenko. 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
 19962001: Ternopil State Pedagogical University, Ternopil, Ukraine (graduate student)
 20012004: Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine (PhD student)
Work
 20042008: Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine (Junior Research Fellow)
 20082010: Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, 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
 20202022: VEGA 2/0127/20 Qualitative properties and bifurcations of differential equations and dynamical systems
 20162019: VEGA 2/0153/16 Qualitative properties and bifurcations of differential equations and dynamical systems
 20182020: ITSM2014+  NFP313011T634 (Výskum v oblasti analýzy heterogénnych dát za účelom predikcie zmeny zdravotného stavu chronických pacientov/Research in the field of heterogeneous data analysis to predict changes in the health status of chronic patients)
 20182020: ITSM2014+  NFP313011T683 (Matematická podpora kvantových technológií/Mathematical support for quantum technologies)
 20132015: VEGA 2/0029/13 Qualitative properties and bifurcations of differential equations and dynamical systems
 20112014: APVV013410 Nonlinear phenomena in continuous and discrete dynamical systems
 20102012: VEGA 2/0124/10 Qualitative property and bifurcation of the differential equations and dynamical systems
 05.200903.2012: Stipendium of the Fond of Stefan Schwartz
 2009: VEGA 2/7140/27 Qualitative property and bifurcation of the differential equations and dynamical systems
 07.200812.2008: Grant No. GP/F26/0154 of the Fundamental Researches State Fund of Ukraine
 03.200812.2008: 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
 20052006: Grant No. 0105U005666 of the Presidium of National Academy of Sciences of Ukraine for young researchers
Attended research stays
 09.200802.2009: National Scholarship Programme of Slovak Republic. Mathematical Institute, Slovak Academy of Sciences, Bratislava
 02.200806.2008: National Scholarship Programme of Slovak Republic. Mathematical Institute, Slovak Academy of Sciences, Bratislava
 25.09.200304.10.2003: Institute of Mathematics, Czech Academy of Sciences, Brno
Research interests
 Boundaryvalue 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;
 Boundaryvalue problems for the functional differential equations of the fractional order;
 Theory of stability.
Reviewing activities
A reviewer for Zentralblatt fur Mathematik
Talks on 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
 International Conference on Differential and Difference Equations and Applications 2019 (ICDDEA 2019) (Lisbon, 15.07.2019)
 Research Workshop of Israel Science Foundation Functional Differential Equations and Applications (FDE 2010) (Ariel, Israel, 27.0804.09.2010)
 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, 1619.09.2008)
 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)
 Workshop2006 "Constructive Methods in Nonlinear Boundary Value Problems" (Sarospatak, Hungary, 710.06.2006)
 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" (Odessa, 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 (Kiev, Ukraine, 27 30.05.2003)
Hobby
I sing in a chorus, play a little bit on a fife and paint
Language skills
Ukrainian, Russian, English, Slovak
ORCID
PUBLONS
GoogleScholar
List of publications
LIST OF PUBLICATIONS
 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. 2021
 N. Dilna, A. Dvurecenskij. Prof. RNDr. Michal Feckan, DrSc. – Sexagenarian?, Math. Slovaca 71 (2021), 265266
 N. Z. Dilna, A. Dvurecenskij. Michal Feckan (on his 60th birthday). Nonlinear Oscillations V. 24, No 1. 2021, pp. 141144
https://www.imath.kiev.ua/~nosc/admin/private/published_files/1335/NOSC13352021241998.pdf
 N. Dilna. On Nonlocal BoundaryValue Problems for HigherOrder Nonlinear 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. 535548 Springer, Cham.
https://doi.org/10.1007/9783030563233_40
 N. Dilna, M. Fečkan and M. Solovyov. DStability 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. Fečkan and A. Rontó. On a class of functional differential equations with symmetries, Symmetry (2019), 11, 1456.
https://www.mdpi.com/20738994/11/12/1456
 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), 116.
https://www.math.uszeged.hu/ejqtde/p7639.pdf
 N. Dilna and M. Feckan. The Stieltjes string model with external load. Applied Mathematics and Computation, Vol. 337 (2018), p. 350359.
 N. Dilna. On the unique solvability of a nonlinear nonlocal boundaryvalue problem for systems of secondorder functional differential equations.
Journal of Mathematical Sciences, Vol. 223 (June, 2017) No. 3, pp. 257272.
 M. Feckan , A. Ronto, N. Dilna. On a kind of symmetric weakly nonlinear ordinary differential systems.
Bulletin des sciences mathématiques, vol. 140, no. 2, (2016), pp. 188230.
 N. Dilna. Unique solvability of second order functional differential equations with nonlocal boundary conditions. E. J. Qualitative Theory of Diff. Equ., No. 14 (2012), pp. 113.
http://www.math.uszeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1187
 N. Dilna and M. Feckan.On symmetric and periodic solutions of parametric weakly nonlinear ODE with timereversal symmetries.
Bulletin of the Belgian Mathematical Society  Simon Stevin, Vol. 18, No. 5 (2011), pp. 896923.
 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.710.
 N. Dilna and A. Ronto. Unique solvability of a nonlinear nonlocal boundaryvalue problem for systems of nonlinear functional differential equations.
Mathematica Slovaca, Vol. 60 (2010), No. 3., pp. 327–338.
 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. 1140.
http://mat76.mat.unimiskolc.hu/~mnotes/contents.php?number=+1+&volume=10
 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. 2228 (in Russian).
 N. Dilna and M. Feckan. Weakly nonlinear and symmetric periodic systems at resonance. Journal Nonlinear Studies, Vol. 16 (2009), No. 2, pp. 2344.
 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. 435445.
 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. 4557.
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 boundaryvalue 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 nonlocal boundary value problem for linear functional differential equations.
Mathematical Modelling and Analysis. Vol. 13 (2008), No. 2, pp. 241250.
 N. Z. Dilna and A. N. Ronto. General conditions for the unique solvability of initialvalue problem for nonlinear functional differential equations.
Ukrainian Mathematical Journal. Vol. 60 (2008), No. 2, pp. 167172.
 A. N. Ronto and N. Z. Dilna. Conditions for the unique solvability of the initialvalue problem for linear secondorder differential equations with argument deviations.
Nonlinear Oscillations. Vol. 9 (2006), No. 4, pp. 535547.
 A. M. Samoilenko, N. Z. Dilna, and A. N. Ronto. Solvability of the Cauchy problem for linear integraldifferential equations with transformed arguments.
Nonlinear Oscillations. Vol. 8 (2005), No. 3, pp. 388403.
 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.unimiskolc.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 righthand 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 functionaldifferential equations.
Ukrainian Mathematical Journal. Vol. 56 (2004), No. 7, pp. 867  884.
 N. Dilnaya and A. Ronto. Multistage iterations and solvability of linear Cauchy problems, Miskolc Mathematical Notes. Vol. 4 (2003), No. 2, pp. 89102.
http://mat76.mat.unimiskolc.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
 M. Feckan, A. Ronto, N. Dilna. On the existence and stability of symmetric solutions in a class of weakly nonlinear systems. 3rd International Conference on Pure and Applied Mathematics.
Van Yuzuncu Yil University, Van, TURKEY, (Van, Turkey, September 35, 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, 15.07.2019)
https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxzYW5kcmFwaW5lbGFzfGd4OjNmMGFkOTAzNjE3ZTQwYmI p.132
 N. Dilna and M. Feckan. About parametric weakly nonlinear ODE with timereversal symmetries. International Conference "Painleve Equations and Related
Topics" (St.Petersburg, Russia, 1723.06.2011)
http://www.pdmi.ras.ru/EIMI/2011/PC/proceedings.pdf  p. 4649.
 N. Dilna and M. Feckan. On parametric weakly nonlinear ODE with timereversal symmetries. International Scientific Conference "Differential equations and their applications"
(Kiev, Ukraine, 810.06.2011) p. 167.
 N. Dilna and A. Ronto. About the unique solvability of a nonlinear nonlocal boundaryvalue problem for systems of nonlinear functionaldifferential
equations. Research Workshop of Israel Science Foundation Functional Differential Equations and Applications (FDE 2010) (Ariel, Israel, 27.0804.09.2010)
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, 0508.08.2010)
http://hk2010.rivok.com//abstracts/pdf/162.pdf
 N. Dilna and M. Feckan. Weakly Nonlinearand Symmetric Periodic Differential Systems //
8 th AIMS International Conference on Dynamical Systems, Differential Equations and Applications (Dresden, Germany,
May 25  28, 2010) P. 41 http://www.math.tudresden.de/aims2010/abstracts/ss74.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, 2729.08.2009)
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 100th anniversary of M. M. Bogolyubov and to the 70th anniversary of M.I. Nahnybida (Chernivtci, Ukraine, 813.06.2009) P. 230231.
 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, 1619.09.2008)  P. 62.
 N. Dilna and A. Ronto. The unique solvability of the initialvalue problem for nonlinear 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 initialvalue problem for nonlinear functionaldifferential 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 initialvalue problem for linear second order functionaldifferential 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. 3334.
 N. Dilna and A. Ronto. On unique solvability of the initialvalue 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 Integraldifferential 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 IntegralDifferential 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 rightsides // 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 integraldifferential equations with (\sigma,\tau)positive rightsides // 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" (IvanoFrankivsk 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 (Chernovtsy, 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 Investigationof Stability of Systems (Kiev, Ukraine, 27 30.05.2003).P. 49.
Research interests
 Boundaryvalue problems for the functional and ordinary differential equations;
 Periodic solutions of the functional and symmetric ordinary differential equations;
 Existence of solutions of the functional differential equations;
 Conditions on a unique solvability of the functional and symmetric ordinary differential equations;
 Boundaryvalue problems for the functional differential equations of the fractional order;
 Theory of stability.

