Mgr. Nataliya 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
    • 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 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.
    Reviewing activities
    A reviewer for Zentralblatt fur Mathematik
    Citations
    • The paper N. Dilnaya and A. Ronto, Multistage iterations and solvability of linear Cauchy problems, Miskolc Mathematical Notes, 4(2), pp. 89--102 (2003) has been cited in such works:
      • J. Sremr. On the innitial value problem for two-dimensional systems of linear functional-differentional equations with monotone operators. Preprints of Academy of Sciences of the Czech Republic. 162/2005, 53 p.
      • J. Sremr, A note on two-dimensional systems of linear differential inequalities with argument deviations, Miskolc Mathematical Notes. 7, No. 2, 171-187, 2006. MR, ZBL MATH
      • J. Sremr, On systems of linear functional differential inequalities, Georgian Mathematical Journal, 13(3), pp. 539-572, 2006. MR, ZBL MATH
      • J. Sremr, On the Cauchy type problem for systems of functional-differential equations. Nonlinear Analysis, Theory, Methods and Applications, 67, no. 12, pp. 3240-3260, 2007. SCI
      • J. Sremr and R. Hakl, On the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators, Nonlinear Oscillations, 10(4), pp. 560-573, 2007. SCOPUS
      • E. I. Bravyi, On the solvability of the Cauchy problem for systems of two liner functional differential equations. Memoirs on Differential Equations and Mathematical Physics, 41, pp. 11-26, 2007. MR, ZBL MATH
      • J. Sremr. On the initial problem for two-dimensional systems of linear functional-differential equations with monotone operators. Fasciculi Mathematici. Nr 37, pp. 87-108, 2007
      • J. Sremr, On the Cauchy type problem for two-dimensional functional-differential systems. Memoirs on Differential Equations and Mathematical Physics, 40, pp. 77-134, 2007. MR, ZBL MATH
      • J. Sremr. Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators. Mathematica Bohemica. 132(3), 263--295, 2007.
      • Z.Oplustil. On constant sign solution (nonpositive) of certain functional differentional inequality. Mathematical models in engineering, biology and medicine. Book Series: AIP Conference Proceedings 1124 pp. 274-283, 2009, SCI
      • A. Lomtatidze, Z. Oplustil and J. Sremr. Nonpositive solutions to a certain functional differential inequality. Nonlinear Oscillations. 12(4), pp. 461-494, 2009
      • J. Sremr. On the initial value problem for two-dimensional linear functional differential systems. Memoirs on Differential Equations and Mathematical Physics, 50, pp. 1-127, 2010.
      • Z. Oplustil. Solvability of a nonlocal boundary value problem for linear functional differential equations. Advances in Difference Equations 2013, 2013:244., WOS
    • The paper A. Ronto, V. Pylypenko, N. Dilna. On the Unique Solvability of a Non-Local Boundary Value Problem for Linear Functional Differential Equations. Mathematical Modelling and Analysis. Vol. 13, No. 2, pp. 241-250 (2008) has been cited in such works:
      • Z. Oplustil, J. Sremr, On a non-local boundary value problem for linear functional differential equations, Electron. J. Qual. Theory Differ. Equ. No. 36, 1-13, 2009., WOS
      • J. Sremr. On the initial value problem for two-dimensional linear functional differential systems. Memoirs on Differential Equations and Mathematical Physics, 50, pp. 1-127, 2010.
      • Domoshnitsky, A., Hakl, R., Pa, B. On the dimension of the solution set to the homogeneous linear functional differential equation of the first order. In Czechoslovak Mathematical Journal, 2012, Vol. 62, No. 4, pp. 1033-1053., WOS
      • M. Ronto, K. Marynets, Parametrization for non-linear problems with integral boundary conditions. Electronic Journal of Qualitative Theory of Differential Equations 2012, No. 99, 1-23
    • The paper 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. has been cited in such work:
      • Li, Y., Huang, F. Levinson's problem on affine-periodic solutions. Advanced Nonlinear Studies, Vol. 15, No. 1, (2014) pp. 241-252., SCOPUS
      • Wang, Hong-ren, Yang, X, Li, Y. Rotating-Symmetric Solutions for Nonlinear Systems with Symmetry. Acta Mathematicae Applicatae Sinica, English Series. Vol. 31, No. 2 (2015) 307312 DOI: 10.1007/s10255-015-0484-2.
      • C. Cheng, F. Huang, Y. Li. Affine-periodic solutions and pseudo affine-periodic solutions for differential equations with exponential dichotomy and exponential trichotomy. Journal of Applied Analysis and Computation 6 (4), (2016), pp. 950-967
      • Wang, C., Yang, X., Li, Y. Affine-Periodic Solutions for Nonlinear Differential Equations. Rocky Mountain Journal of Mathematics. First available in Project Euclid: 2 February 2015, to appear 2016
    • The paper A. M. Samoilenko, N. Z. Dina, 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 has been cited in such work:
      • A. A. Boichuk, I. V. Gaishun, V. A. Ilin, N. A. Izobov, E. F. Mishchenko, Yu. A. Mitropolskii, N. A. Perestyuk, N. Kh. Rozov. Anatolii Mikhailovich Samoilenko. A tribute in honor of his seventieth birthday. Differential Equations, (2008), 44 (2), pp 150-160.
    • The paper 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. has been cited in such work:
      • A. Dutkiewicz. On the existence of solutions of ordinary differential equations in banach spaces. Mathematica Slovaca. ISSN 0139-9918, 2015, vol. 65, no. 3, p. 573-582.
    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
    1. Research Workshop of Israel Science Foundation Functional Differential Equations and Applications (FDE 2010) (Ariel, Israel, 27.08-04.09.2010)
    2. 8 th AIMS International Conference on Dynamical Systems, Differential Equations and Applications (Dresden, Germany, May 25 - 28, 2010)
    3. Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine (Santiago de Compostela, Spain, 16-19.09.2008)
    4. International Conference on the Occasion of the 150th Birthday of A. M. Lyapunov "Lyapunov Memorial Conference" (Kharkiv, Ukraine, 24 - 30.06.2007)
    5. The 12th International Conference "Mathematical Modelling and Analysis" (Trakai, Lithuania, 30.05 - 2.06.2007)
    6. The 8th International Crimean mathematical school "Method of Lyapunov Functions and Its Applications" (Crimea, Alushta, 11 - 17.09.2006)
    7. Conference on Differential and Difference Equations (Brno, Czech Republic, 5 - 8.09.2006)
    8. Workshop-2006 "Constructive Methods in Nonlinear Boundary Value Problems" (Sarospatak, Hungary, 7-10.06.2006)
    9. The 11th International Scientific Conference dedicated to memory of academician M. M. Kravchuk (Kyiv, National Technical University of Ukraine, 18 - 21.05.2006)
    10. XI Konferencija "Matematyka w naukah technicznych i przyrodniczych" (Krynica, Poland, 30.09.2005 - 03.10.2005)
    11. International conference "Integral Equations and Their Applications" (Odessa, Ukraine, 29.06 -4.07.2005)
    12. International conference "Differential Equations and Their Applications" (Kyiv, Ukraine, 6.06 - 12.06.2005)
    13. Young scientists conference "Actual Problems of Mechanics and Mathematics - 2005" dedicated to memory of academician Ya. S. Pidstryhach (Lviv, Ukraine, 24 - 27.05.2005)
    14. VIII Konferencija "Matematyka w naukah technicznych i przyrodniczych" (Krynica, Poland, 30.09.2004- 03.10.2004)
    15. The 7th International Crimean mathematical school "Method of Lyapunov Functions and Its Applications" (Crimea, Alushta, 11 - 18.09.2004)
    16. The 10th International Scientific Conference Dedicated to the Memory of Academician M. M. Kravchuk (Kyiv, National Technical University of Ukraine, 13 - 15.05.2004)
    17. VIth International Scientific Conference Dedicated to the Memory of M. M. Bogoliubov (Chernovtsy, Ukraine, 26 - 30.08.2003)
    18. The 7th Colloquium on the Qualitative Theory of Differential Equations (Szeged, Hungary, Bolyai Institute, University of Szeged, 14 - 18.07.2003)
    19. International Mathematical Conference on Differential Equations and Applications (Zilina, Slovakia, 30.06.2003 - 04.07.2003)
    20. International Scientific Conference on Modelling and Investigation of Stability of Systems (Kiev, Ukraine, 27- 30.05.2003)
    Hobby
    I sing in a chorus and I play a little bit on a fife
    Language skills
    Ukrainian, Russian, English, Slovak

List of publications
LIST OF PUBLICATIONS
  1. 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.
  2. 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.
  3. 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
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. http://mat76.mat.uni-miskolc.hu/~mnotes/contents.php?number=+1+&volume=10
  9. 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).
  10. 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.
  11. 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.
  12. 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.
  13. http://www.jeomj.rmi.acnet.ge/memoirs/vol44/contents.htm
  14. 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).
  15. 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.
  16. http://inga.vgtu.lt/~art/
  17. N. Z. Dilna and A. N. Ronto. General conditions of the unique solvability of the Cauchy problem for systems of nonlinear functional-differential equations. Ukrainian Mathematical Journal. Vol. 60 (2008), No. 2, pp. 167-172.
  18. A. N. Ronto and N. Z. Dilna. Unique solvability conditions of the initial value problem for linear differential equations with argument deviations. Nonlinear Oscillations. Vol. 9 (2006), No. 4, pp. 535-547.
  19. 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.
  20. 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
  21. 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).
  22. N. Z. Dilna and A. N. Ronto. New solvability conditions for the Cauchy problem for systems of linear functional differential equations. Ukrainian Mathematical Journal. Vol. 56 (2004), No. 7, pp. 867 - 884.
  23. 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
  24. PREPRINTS
  25. 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
  26. 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
  27. LIST OF ABSTRACTS
  28. 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.
  29. 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.
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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.
  35. 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.
  36. 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.
  37. 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
  38. 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.
  39. 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.
  40. 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)
  41. 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)
  42. 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.
  43. 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.
  44. 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.
  45. 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.
  46. 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.
  47. 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.
  48. 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.
  49. 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.
  50. 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.
  51. 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.
  52. 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.
  53. 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.
  54. 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.