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.