Monday, June 16, 2008

List of Publications

  1. 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.
  2. N. Dilna, M. Fečkan. About the uniqueness and stability of symmetric and periodic solutions of weakly nonlinear ordinary differential equations. Dop. Nats. Akad. Nauk Ukrainy, (2009), No. 5, pp. 22- 28 (in Russian).
  3. N. Dilna, M. Fečkan. On the uniqueness and stability of symmetric and periodic solutions of weakly nonlinear ordinary differential equations. Miskolc Mathematical Notes. Vol. 10 (2009), No. 1, pp. 11-40. URL: http://mat76.mat.uni-miskolc.hu/~mnotes/contents.php?number=+1+&volume=10
  4. N. Dilna and M. Fečkan. Weakly non-linear and symmetric periodic systems at resonance. Journal Nonlinear Studies, Vol. 16 (2009), No. 2, pp. 23-44. URL: www.nonlinearstudies.com/old/journal/Members/vol_16,_no.2,_2009.htm
  5. N. Dilna, 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.
  6. 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. URL: http://www.jeomj.rmi.acnet.ge/memoirs/vol44/contents.htm
  7. N. Dilna, A. Ronto, V. Pylypenko. Some coditions for the unique solvabilityof a nonlocal boundary-value problem for linear functional differential equations. Dop. Nats. Akad. Nauk Ukrainy, (2008), No. 6, pp. 13- 18 (in Ukrainian).
  8. 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 (2008), No. 2, pp. 241-250. URL: http://inga.vgtu.lt/~art/
  9. N. Z. Dilna, 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.
  10. A. N. Ronto, N. Z. Dilna. Unique solvability conditions of the initialvalue problem for linear differential equations with argument deviations. Nonlinear Oscillations. Vol. 9 (2006), No. 4, pp. 535-547.
  11. 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.
  12. 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. URL: http://mat76.mat.uni-miskolc.hu/~mnotes/contents.php?volume=5&number=2#article104
  13. 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. Dop. Nats. Akad. Nauk Ukrainy, (2004), No. 2, pp. 29- 35 (in Russian).
  14. 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.
  15. N. Dilnaya and A. Ronto. Multistage iterations and solvability of linear Cauchy problems,. Miskolc Mathematical Notes. Vol. 4 (2003), No. 2, pp. 89-102. URL: http://mat76.mat.uni-miskolc.hu/~mnotes/contents.php?volume=4&number=2#article81

    Preprints

N. Dilna, 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
  • Nataliya Dilna, Michal Fečkan. 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. www.mat.savba.sk/preprints/2008.htm
  • Nataliya Dilna, Michal Fečkan. 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. www.mat.savba.sk/preprints/2009.htm
Citations

The paper [15] N. Dilnaya and A. Ronto. Multistage iterations and solvability of linear Cauchy problems, Miskolc Mathematical Notes. Vol. 4 (2003), No. 2, pp. 89-102
has been cited in such works:
  1. J. Šremr. 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.
  2. J. Šremr. 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
  3. J. Šremr. On systems of linear functional differential inequalities, Georgian Mathematical Journal. 13(3), pp. 539-572, 2006. MR, ZBL MATH
  4. J. Šremr. 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
  5. J. Šremr 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
  6. 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
  7. J. Šremr. 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
  8. J. Šremr. Solvabiliy conditions of the Cauchy problem for two-dimensional systems of linear functional-differential equations with monotone operators. Mathematica Bohemica 132(2), 263-295, 2007.
  9. 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
  10. 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
  11. A. Lomtatidze, Z. Opluštil та J. Šremr. Nonpositive solutions to a certain functional differential inequality. Nonlinear Oscillations. 12(4) , pp. 461-494, 2009
  12. 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.

The paper [8] 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 (2008), No. 2, pp. 241-250.
has been cited in such work:
  • Z. Opluštil, J. Šremr, On a non-local boundary value problem for linear functional differential equations, Electron. J. Qual. Theory Differ. Equ. (2009), No. 36, 1-13.

List of Abstracts

  1. 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, 29.08- 03.09.2010)
  2. N. Z. Dilna. Unique Solvability of the Initial Value Problem for Nonlinear Functional Di erential Equations. Mathematics and life sciences: possibilities, interlacements and limits (Kyiv, Ukraine, August 05 - 08, 2010) www.hk2010.rivok.com//abstracts/pdf/162.pdf
  3. 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 www.math.tu-dresden.de/aims2010/abstracts/ss7-4.pdf
  4. N. Dilna and M. Fečkan. On the weakly nonlinear and symmetric periodic systems at resonance // International Conference - Ukrainian Mathematical Congress - 2009. Dedicated to the Centennial of Nikolai N. Bogoljubov.(Kyiv, Institute of Mathematics of NAS of UKraine, 27 - 29.08.2009)
  5. N. Dilna and M. Fečkan. 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. Bogoljubov and 70-th anniversary of M.I.Nahnybida (Chernivtsi, Ukraine, 8 - 13.06.2009) P. 230-231.
  6. N. Dilna and M. Fečkan. 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.
  7. 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.
  8. 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
  9. 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" (Kharkiv, Ukraine, 24 - 30.06.2007) - Karazin Kharkiv National University. - P. 33-34.
  10. 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.
  11. 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)
  12. 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, Czhech Republic, 5 - 8.09.2006)
  13. 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.
  14. N. Z. Dilna and A. M. Ronto. // The 11th International Scientiffic Conference dedicated to memory of academician M. M. Kravchuk (Kyiv, National Technical University of Ukraine, 17 - 21.05.2006) - National Technical University. - P. 126.
  15. 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). - Odesa National University. - P. 48.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. N. Z. Dilnaya, A. N. Ronto. About unique solvability of the Cauchy problem for linear functional differential equations with (\sigma, tau)-positive rightside. // International Scientific Conference on Modelling and Investigationof Stability of Systems (Kiev, Ukraine, 27- 30.05.2003).-P. 49.

Talks on the scientific seminars

  1. Mathematical seminar "Aká si mi krásna", Matej Bel University (Banská Bystrica, Slovak Republic, 19.05.2009)
  2. Seminar on Differential Equations and Dynamical Systems, Faculty of Natural Sciences, Comenius University (Bratislava, Slovak Republic, 27.02.2009)
  3. Seminar on the Difference and Differential Equations, University of Žilina (Žilina, Slovak Republic, 09.06.2008)
  4. Seminar on the Quantum Logics, Center of Excellence of the Slovak Academy of Sciences CE PI, Mathematical Institute of the Slovak Academy of Sciences (Bratislava, Slovak Republic, 29.02.2008)
  5. Seminar on the Department of Differential Equations and Nonlinear Oscillations, Institute of Mathematics, National Academy of Sciences of Ukraine (Kiev, Ukraine, 12.11.2007)
  6. Seminar on the Department of Differential Equations and Nonlinear Oscillations, Institute of Mathematics, National Academy of Sciences of Ukraine (Kiev, Ukraine, 25.10.2005)
  7. Seminar on the Department of Differential Equations and Nonlinear Oscillations, Institute of Mathematics, National Academy of Sciences of Ukraine (Kiev, Ukraine, 20.09.2004)
  8. 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

  • 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 Madicine (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, Czhech 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" (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 (Chernivtsi, 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)

Research interests

  • Boundary-value problems for the functional-differential equations;
  • Periodic solutions of the symmetric ordinary differential equations and differential equations at resonance;
  • Stability of the solutions of the symmetric ordinary differential equations.

Reviewing activities

A reviewer for ZentralBlatt fur Mathematik


Grants and Post-Docs

Post-Doc Position
  • Since 2009: post-doc position in Mathematical Institute of the Slovak Academy of Sciences under support of the Fond of Stefan Schwarz
Grants
  • 09.2008-02.2009: Grant of National Scholarship Programme of Slovak Republic.
  • 07.2008-12.2008: Grant of the Fundamental Researches State Fund
  • 03.2008-12.2008: Grant of the Presidium of National Academy of Sciences of Ukraine for young researchers.
  • 02.2008-06.2008: Grant of National Scholarship Programme of Slovak Republic.
  • 2007: Grant No. 0107U003322 of the Ukrainian State Fund for Fundamental Research.
  • 2005-2006: Grant No. 0105U005666 of the Presidium of National Academy of Sciences of Ukraine for young researchers.

Work

  • 2004-2008: Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine (Junior Research Fellow)
  • 2008-2010: Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine (Research Fellow)
  • Current: Mathematical Institute, Slovak Academy of Sciences, Bratislava