Zoznam pracovníkov MÚ SAV, v. v. i.

• Detašované pracovisko Matematického ústavu SAV v Košiciach
• Inštitút matematiky a informatiky MÚ SAV v B. Bystrici
• Oddelenie informatiky Matematického ústavu SAV

Dilna, Natália Mgr., PhD.

Národné projekty

• Kvalitatívne vlastnosti a oscilácie diferenciálnych rovníc a dynamických systémov
  Program: VEGA
  Doba trvania: 1.1.2024 - 31.12.2027

• Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov
  Program: VEGA
  Doba trvania: 1.1.2020 - 31.12.2023

• Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov
  Program: VEGA
  Doba trvania: 1.1.2016 - 31.12.2019

• Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov
  Program: VEGA
  Doba trvania: 1.1.2013 - 31.12.2015

• Nelineárne javy v spojitých a diskrétnych dynamických systémoch
  Program: APVV
  Doba trvania: 1.5.2011 - 31.5.2014

• Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov
  Program: VEGA
  Doba trvania: 1.1.2010 - 31.12.2012

• Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov A f- prvky
  Program: VEGA
  Doba trvania: 1.1.2007 - 1.12.2009

Publikácie

• RONTO, A. - DILNA, Natália. Multistage iterations and solvability of linear Cauchy Problems. In Miskolc Mathematical Notes, 2003, vol. 4, no. 2, s. 89-102. ISSN 1787-2413.
• DILNA, Natália - RONTO, A. General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations. In Mathematica Bohemica, 2008, vol. 133, p. 435-445. ISSN 0862-7959.
• DILNA, Natália. On unique solvability of the initial value problem for nonlinear functional differential equations. In Memoirs on Differential Equations and Mathematical Physics, 2008, vol. 44, s. 45-57. ISSN 1512-0015.
• RONTO, A. - PYLYPENKO, V. - DILNA, Natália. On the unique solvability of a non-local boundary value problem for linear functional differential equations. In Mathematical Modelling and Analysis, 2008, vol. 13, s. 241-250. (2007: 0.408 - SJR, Q3 - SJR). ISSN 1392-6292.
• DILNA, Natália - FEČKAN, Michal. About the uniqueness and stability of symmetric and periodic solutions of weakly nonlinear ordinary differential equations. In Dopovidi Natsionalnoi Akademii Nauk Ukraini, 2009, vol. 5, s. 22-28. ISSN 1025-6415.
• DILNA, Natália - FEČKAN, Michal. Weakly nonlinear and symmetric periodic systems at resonance. In Nonlinear Studies, 2009, vol. 16, no. 2, s. 23-44. ISSN 1359- 8678.
• DILNA, Natália - FEČKAN, Michal. On the uniqueness, stability and hyperbolicity of symmetric and periodic solutions of weakly nonlinear ordinary differential equations. In Miskolc Mathematical Notes, 2009, vol. 10, no. 1, s. 11-40. ISSN 1787-2405.
• DILNA, Natália - RONTO, A. Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations. In Mathematica Slovaca, 2010, vol. 60, no. 3, p. 327-338. (2009: 0.308 - IF, Q4 - JCR, 0.248 - SJR, Q3 - SJR). ISSN 0139-9918. Dostupné na: <a href="https://doi.org/10.2478/s12175-010-0015-9">https://doi.org/10.2478/s12175-010-0015-9</a>
• DILNA, Natália. Unique Solvability of the Initial Value Problem for Nonlinear Functional Differential Equations. In Mathematics and life sciences: possibilities, interlacements and limits (Kyiv, Ukraine, 05-08.08.2010), 2010. Dostupné na internete: <a href="http://hk2010.rivok.com//abstracts/pdf/162.pdf">http://hk2010.rivok.com//abstracts/pdf/162.pdf</a>
• DILNA, Natália - FEČKAN, Michal. Weakly Nonlinearand Symmetric Periodic Differential Systems // 8-th AIMS International Conference on Dynamical Systems. In Differential Equations and Applications (Dresden, Germany, May 25 - 28, 2010), 2010. Dostupné na internete: <a href="http://www.math.tu-dresden.de/aims2010/abstracts/ss7-4.pdf">http://www.math.tu-dresden.de/aims2010/abstracts/ss7-4.pdf</a>
• DILNA, Natália - RONTO, A. About the unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional-differential equations. In Research Workshop of Israel Science Foundation Functional Differential Equations and Applications (FDE 2010) (Ariel, Israel, 27.08-04.09.2010), 2010. Dostupné na internete: <a href="http://ariel.ac.il/projects/math/adom/abs.pdf">http://ariel.ac.il/projects/math/adom/abs.pdf</a>
• DILNA, Natália - FEČKAN, Michal. On symmetric and periodic solutions of parametric weakly nonlinear ODE with time-reversal symmetries. In Bulletin of the Belgian Mathematical Society, 2011, vol. 18, no. 5, s. 896-923. (2010: 0.341 - IF, Q4 - JCR, 0.501 - SJR, Q3 - SJR, karentované - CCC). (2011 - Current Contents). ISSN 1370-1444.
• DILNA, Natália. About symmetric solutions of a class of functional differential equations. In Reports of the National Academy of Sciences of Ukraine, 2011, no. 9, s. 7-10. ISSN 1025-6415.
• DILNA, Natália - FEČKAN, Michal. About parametric weakly nonlinear ODE with time-reversal symmetries. In International Conference "Painleve Equations and Related Topics. - Rusko, 2011, s. 46-49.
• DILNA, Natália - FEČKAN, Michal. On parametric weakly nonlinear ODE with time-reversal symmetries. In International Scientific Conference "Differential equations and their applications", s. 167.
• DILNA, Natália. Unique solvability of second order functional differential equations with non-local boundary conditions : <a href="http://www.math.u-szeged.hu/ejqtde/p1187.pdf.">http://www.math.u-szeged.hu/ejqtde/p1187.pdf.</a> In Electronic Journal of Qualitative Theory of Differential Equations, 2012, no. 14, s. 1-13. (2011: 0.557 - IF, Q3 - JCR, 0.842 - SJR, Q2 - SJR, karentované - CCC). (2012 - Current Contents). ISSN 1417-3875.
• FEČKAN, Michal - RONTÓ, András - DILNA, Natália. On a kind of symmetric weakly non-linear ordinary differential systems. In Bulletin des sciences mathématiques, 2016, vol. 140, no. 2, p. 188-230. (2015: 0.664 - IF, Q3 - JCR, 1.965 - SJR, Q1 - SJR, karentované - CCC). (2016 - Current Contents). ISSN 0007-4497. Dostupné na: <a href="https://doi.org/10.1016/j.bulsci.2015.11.003">https://doi.org/10.1016/j.bulsci.2015.11.003</a>
• DILNA, Natália. On the unique solvability of a nonlinear nonlocal boundary-value problem for systems of second-order functional differential equations. In Journal of Mathematical Sciences, 2017, vol. 223, no. 3, p. 257-272. (2016: 0.265 - SJR, Q3 - SJR). ISSN 1072-3374. Dostupné na: <a href="https://doi.org/10.1007/s10958-017-3352-1">https://doi.org/10.1007/s10958-017-3352-1</a>
• DILNA, Natália** - FEČKAN, Michal. The Stieltjes string model with external load. In Applied Mathematics and Computation, 2018, vol. 337, p. 350-359. (2017: 2.300 - IF, Q1 - JCR, 1.065 - SJR, Q1 - SJR, karentované - CCC). (2018 - Current Contents). ISSN 0096-3003. Dostupné na: <a href="https://doi.org/10.1016/j.amc.2018.05.026">https://doi.org/10.1016/j.amc.2018.05.026</a>
• DILNA, Natália** - FEČKAN, Michal - SOLOVYOV, Mykola - WANG, JinRong. Symmetric nonlinear functional differential equations at resonance. In Electronic Journal of Qualitative Theory of Differential Equations, 2019, no. 76, p. 1-16. (2018: 1.065 - IF, Q1 - JCR, 0.482 - SJR, Q2 - SJR, karentované - CCC). (2019 - Current Contents). ISSN 1417-3875. Dostupné na: <a href="https://doi.org/10.14232/ejqtde.2019.1.76">https://doi.org/10.14232/ejqtde.2019.1.76</a>
• DILNA, Natália - FEČKAN, Michal - RONTÓ, András. On a class of functional differential equations with symmetries. In Symmetry-basel, 2019, vol. 11, issue 12, art. no. 1456. (2018: 2.143 - IF, Q2 - JCR, 0.287 - SJR, Q2 - SJR, karentované - CCC). (2019 - Current Contents, WOS, SCOPUS). ISSN 2073-8994. Dostupné na: <a href="https://doi.org/10.3390/sym11121456">https://doi.org/10.3390/sym11121456</a>
• DILNA, Natália - FEČKAN, Michal** - SOLOVYOV, Mykola. D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations. In Symmetry-basel, 2020, vol. 12, no. 1761, p. 1-19. (2019: 2.645 - IF, Q2 - JCR, 0.365 - SJR, Q2 - SJR, karentované - CCC). (2020 - Current Contents). ISSN 2073-8994. Dostupné na: <a href="https://doi.org/10.3390/sym12111761">https://doi.org/10.3390/sym12111761</a>
• DILNA, Natália. On Non-local Boundary-Value Problems for Higher-Order Non-linear Functional Differential Equations. In Springer Proceedings in Mathematics and Statistics 333 : Differential and Difference Equations with Applications. - Springer, 2020, 2020, p. 535-548. ISBN 978-3-030-56323-3. Dostupné na: <a href="https://doi.org/10.1007/978-3-030-56323-3_40">https://doi.org/10.1007/978-3-030-56323-3_40</a>
• DILNA, Natália - DVUREČENSKIJ, Anatolij. Prof. RNDr. Michal Fečkan, Dr.Sc. - Sexagenarian? In Mathematica Slovaca, 2021, roč. 71, č. 2, s. 265-266. (2020: 0.770 - IF, Q3 - JCR, 0.445 - SJR, Q2 - SJR). ISSN 0139-9918. Dostupné na: <a href="https://doi.org/10.1515/ms-2017-0465">https://doi.org/10.1515/ms-2017-0465</a>
• DILNA, Natália - DVUREČENSKIJ, Anatolij. Michal Fečkan (on his 60th birthday). In Nonlinear Oscillations, 2021, vol. 24, no. 1, p. 141-144. ISSN 1562-3076.
• DILNA, Natália** - FEČKAN, Michal. Exact Solvability Conditions for the Non-Local Initial Value Problem for Systems of Linear Fractional Functional Differential Equations. In Mathematics, 2022, vol. 10, art. no. 1759. (2021: 2.592 - IF, Q1 - JCR, 0.538 - SJR, Q2 - SJR, karentované - CCC). (2022 - Current Contents). ISSN 2227-7390. Dostupné na: <a href="https://doi.org/10.3390/math10101759">https://doi.org/10.3390/math10101759</a>
• DILNA, Natália. D-stability of the model of the Stieltjes string related to the functional differential equations. In Examples and Counterexamples, 2022, vol. 2, art. no. 100092. ISSN 2666-657X. Dostupné na: <a href="https://doi.org/10.1016/j.exco.2022.100092">https://doi.org/10.1016/j.exco.2022.100092</a>
• DILNA, Natália** - GROMYAK, M - LESHCHUK, S. Unique Solvability of the Boundary-Value Problems for Nonlinear Fractional Functional Differential Equations. In Journal of Mathematical Sciences, 2022, vol. 265, no. 4, p. 577-588. (2021: 0.357 - SJR, Q3 - SJR). ISSN 1072-3374. Dostupné na: <a href="https://doi.org/10.1007/s10958-022-06072-8">https://doi.org/10.1007/s10958-022-06072-8</a>
• DILNA, Natália. Exact solvability conditions for the model with a discrete memory effect. In International Conference on Mathematical Analysis and Aplications in Science and Engineering - Book of Extended Abstracts : ICMA2SC´22. Eds. Carla M.A. Pinto, Jorge Mendonca. - Porto, Portugal : ISEP/P.PORTO, 2022, p. 405-407. ISBN 978-989-53496-3-0.
• DILNA, Natália. D-stability of the initial value problem for symmetric nonlinear functional differential equations. In Book of Abstracts : EQUADIFF 15 [elektronický zdroj], 2022, p. 157. Názov z internetu. Požaduje sa internet. Dostupné na internete: <a href="https://conference.math.muni.cz/equadiff15/files/book-of-abstracts.pdf">https://conference.math.muni.cz/equadiff15/files/book-of-abstracts.pdf</a>
• DILNA, Natália. Unique Solvability of the Initial-Value Problem for Fractional Functional Differential Equations-Pantograph-Type Model. In Fractal and Fractional, 2023, vol. 7, no. 1, art. no. 65. (2022: 5.4 - IF, Q1 - JCR, 0.627 - SJR, Q2 - SJR). ISSN 2504-3110. Dostupné na: <a href="https://doi.org/10.3390/fractalfract7010065">https://doi.org/10.3390/fractalfract7010065</a> (VEGA 2/0127/20 : Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov)
• DILNA, Natália - FEČKAN, Michal - RONTÓ, András**. Solvability of the symmetric nonlinear functional differential equations. In Mathematical Methods in the Applied Sciences, 2023, vol. 46, p. 18975-18984. (2022: 2.9 - IF, Q1 - JCR, 0.628 - SJR, Q1 - SJR). ISSN 0170-4214. Dostupné na: <a href="https://doi.org/10.1002/mma.9603">https://doi.org/10.1002/mma.9603</a> (VEGA 2/0127/20 : Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov)
• DILNA, Natália** - LESHCHUK, Svitlana. D-stability of the model of the Stieltjes string. In Applicable Analysis, 2023, vol. 102, no. 18, p. 5157-5169. (2022: 1.1 - IF, Q3 - JCR, 0.535 - SJR, Q2 - SJR). ISSN 0003-6811. Dostupné na: <a href="https://doi.org/10.1080/00036811.2023.2168654">https://doi.org/10.1080/00036811.2023.2168654</a> (VEGA 2/0127/20 : Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov)
• DILNA, Natália. Precise Conditions on the Unique Solvability of the Linear Fractional Functional Differential Equations Related to the ς-Nonpositive Operators. In Fractal and Fractional, 2023, vol. 7, no. 10, art. nr. 720. (2022: 5.4 - IF, Q1 - JCR, 0.627 - SJR, Q2 - SJR). ISSN 2504-3110. Dostupné na: <a href="https://doi.org/10.3390/fractalfract7100720">https://doi.org/10.3390/fractalfract7100720</a> (VEGA 2/0127/20 : Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov)
• DILNA, Natália - FEČKAN, Michal - WANG, JinRong. Note on quaternion linear dynamical systems. In Nonlinear Oscillations, 2023, vol. 26, no. 1, p. 22-32, art. nr. 1413. ISSN 1562-3076. Dostupné na internete: <a href="https://imath.kiev.ua/~nosc/web/show_article.php?article_id=1413&lang=en">https://imath.kiev.ua/~nosc/web/show_article.php?article_id=1413&lang=en</a> (VEGA 2/0127/20 : Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov)
• DILNA, Natália. General exact solvability conditions for the initial value problems for linear fractional functional differential equations. In Archivum Mathematicum, 2023, vol. 59, p. 11-19. (2022: 0.6 - IF, 0.218 - SJR, Q4 - SJR). ISSN 0044-8753. Dostupné na: <a href="https://doi.org/10.5817/AM2023-1-11">https://doi.org/10.5817/AM2023-1-11</a> (VEGA 2/0127/20 : Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov)
• DILNA, Natália. General Exact Solvability Conditions for the Initial Value Problems for Linear Fractional Functional Differential Equations : Abstract. In IWOTA 2023. - Helsinki, Finland : University of Helsinki, 2023, 2023, p. 69-70. (VEGA 2/0127/20 : Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov. 34th International Workshop on Operator Theory and its Applications)
• DILNA, Natália** - FEKETE, Gusztáv - LANGEROVÁ, Martina - TÓTH, Balázs. Ulam-Hyers and Generalized Ulam-Hyers Stability of Fractional Differential Equations with Deviating Arguments. In Mathematics, 2024, vol. 12, no. 21, art. nr. 3418. (2023: 2.3 - IF, Q1 - JCR, 0.475 - SJR, Q2 - SJR). ISSN 2227-7390. Dostupné na: <a href="https://doi.org/10.3390/math12213418">https://doi.org/10.3390/math12213418</a> (VEGA 2/0062/24 : Kvalitatívne vlastnosti a oscilácie diferenciálnych rovníc a dynamických systémov)
• DILNA, Natália** - FEČKAN, Michal - WANG, JinRong. A Note on Quaternion Linear Dynamical Systems. In Journal of Mathematical Sciences, 2024, vol. 278, no. 6, pp. 950-962. (2023: 0.302 - SJR, Q3 - SJR). ISSN 1072-3374. Dostupné na: <a href="https://doi.org/10.1007/s10958-024-06973-w">https://doi.org/10.1007/s10958-024-06973-w</a> (VEGA 2/0127/20 : Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov)
• DILNA, Natália - LANGEROVÁ, Martina. Ulam-Hyers and generalized Ulam-Hyers stability of fractional functional integro-differential equations. In IFAC-PapersOnLine, 2024, vol. 58, no. 12, pp. 280-285. (2023: 0.365 - SJR). ISSN 2405-8963. Dostupné na: <a href="https://doi.org/10.1016/j.ifacol.2024.08.203">https://doi.org/10.1016/j.ifacol.2024.08.203</a> (VEGA 2/0062/24 : Kvalitatívne vlastnosti a oscilácie diferenciálnych rovníc a dynamických systémov)
• DILNA, Natália - LANGEROVÁ, Martina. Ulam-Hyers and Generalized Ulam-Hyers Stability of Fractional Functional Integro-Differential Equations : Abstract. In ICFDA 2024 : Book of Abstracts. - Bordeaux, France : IFAC, France, 2024, 2024, p. 308-313. Dostupné na internete: <a href="https://ifac.papercept.net/conferences/scripts/rtf/FDA24_ContentListWeb_3.html">https://ifac.papercept.net/conferences/scripts/rtf/FDA24_ContentListWeb_3.html</a> (IFAC Conference on Fractional Differentiation and its Applications)
• DILNA, Natália. D-stability of the model of the Stieltjes string : Abstract. In Equadiff 2024 : Book of Abstracts. - Karlstad, Sweden : Karlstads Universitet, 2024, 2024, no. 1D340. Dostupné na internete: <a href="https://www.kau.se/files/2024-06/Book_of_Abstracts%28a%29.pdf">https://www.kau.se/files/2024-06/Book_of_Abstracts%28a%29.pdf</a> (EQUADIFF 2024)
• FEKETE, Gusztav** - MÁTÉ, Márton - POPA-MÜLLER, Izolda - WANG, Hai-Qiao - DILNA, Natália - NEMOGA, Karol. Computational Wear Prediction in Total Knee Replacements as a FUnction of Replacement Size. In Material Strength and Applied Mechanics : Proceedings. 59.Advances in Transdisciplinary Engineering, 2024, vol. 59, p. 494-500. Dostupné na: <a href="https://doi.org/10.3233/ATDE240585">https://doi.org/10.3233/ATDE240585</a> (VEGA 2/0062/24 : Kvalitatívne vlastnosti a oscilácie diferenciálnych rovníc a dynamických systémov. VEGA 2/0119/23 : Teória čísel a jej aplikácie. APVV-19-0220 : Ontologická reprezentácia pre bezpečnosť informačných systémov. MSAM 2024 : International Conference)
• JIANG, Xinyan - BÍRÓ, István - WANG, Hai-Qiao - DILNA, Natália - NEMOGA, Karol - FEKETE, Gusztáv**. Experimental Study on Ground Reaction Force Parameters with Regard to Novice and Recreational Runners. In Material Strength and Applied Mechanics : Proceedings. 59.Advances in Transdisciplinary Engineering. - Amsterdam, Netherlands : IOS Press, 2024, 2024, vol. 59, p. ISBN 978-1-64368-547-2. Dostupné na: <a href="https://doi.org/10.3233/ATDE240590">https://doi.org/10.3233/ATDE240590</a> (MSAM 2024 : International Conference)
• LESHCHUK, S. - DILNA, Natália - GROD, I. - RADCHENKO, O. - HNOIOVA, T. The implementation of STE(A)M education through Scratch projects. In Journal of Physics: Conference Series : ICon-MaSTEd 2024 - XVI International Conference on Mathematics, Science and Technology Education, 2024, vol. 2871, art. nr. 012018, 15 p. (2023: 0.18 - SJR). ISSN 1742-6588. Dostupné na: <a href="https://doi.org/10.1088/1742-6596/2871/1/012018">https://doi.org/10.1088/1742-6596/2871/1/012018</a> (VEGA 2/0062/24 : Kvalitatívne vlastnosti a oscilácie diferenciálnych rovníc a dynamických systémov)