Mgr. Natalia Dilna, PhD.


Scientific degree: PhD
Place of birth: Ternopol, Ukraine
Mailing address: Mathematical Institute
Slovak Academy of Sciences
Stefanikova 49 Str.
Bratislava 81473
Slovak Republic
E-mail:chiefnatalie(at)gmail.com
Tel: +421 2 57510409
Fax: +421 2 52497316


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 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. 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, Kiev, Ukraine (PhD student)
    Work
    • 2004-2008: Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine (Junior Research Fellow)
    • 2008-2009: 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
    • 2020-2022: 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
    • 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;
    • Theory of stability.
    Reviewing activities
    A reviewer for Zentralblatt fur Mathematik
    Citations
List of publications
LIST OF PUBLICATIONS
  1. 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
  2. N. Dilna, A. Dvurecenskij, Prof. RNDr. Michal Feckan, DrSc. Sexagenarian?, Math. Slovaca 71 (2021), 265-266
  3. 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
  4. 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
  5. N. Dilna, M. Fekan 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
  6. N. Dilna, M. Fekan and A. Ront. On a class of functional differential equations with symmetries, Symmetry (2019), 11, 1456. https://www.mdpi.com/2073-8994/11/12/1456
  7. 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://www.math.u-szeged.hu/ejqtde/p7639.pdf
  8. N. Dilna and M. Feckan. The Stieltjes string model with external load. Applied Mathematics and Computation, Vol. 337 (2018), p. 350-359.
  9. 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.
  10. M. Feckan , A. Ronto, N. Dilna. On a kind of symmetric weakly non-linear ordinary differential systems. Bulletin des sciences mathmatiques, vol. 140, no. 2, (2016), pp. 188-230.
  11. 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.
    http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1187
  12. 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.
  13. 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.
  14. 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. 327338.
  15. 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.
    http://mat76.mat.uni-miskolc.hu/~mnotes/contents.php?number=+1+&volume=10
  16. 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).
  17. 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.
  18. 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.
  19. 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.
  20. http://www.jeomj.rmi.acnet.ge/memoirs/vol44/contents.htm
  21. 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).
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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
  27. 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).
  28. 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.
  29. 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
  30. PREPRINTS
  31. 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
  32. 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
  33. LIST OF ABSTRACTS
  34. 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
  35. 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
  36. 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.
  37. 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.
  38. 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
  39. 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
  40. 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.tu-dresden.de/aims2010/abstracts/ss7-4.pdf
  41. 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
  42. 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.
  43. 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.
  44. 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.
  45. 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
  46. 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.
  47. 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.
  48. 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)
  49. 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)
  50. 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.
  51. 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.
  52. 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.
  53. 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.
  54. 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.
  55. 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.
  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.
  57. 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.
  58. 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.
  59. 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.
  60. 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.
  61. 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.
  62. 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.
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Research interests
  • Boundary-value 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;
  • Theory of stability.