Opuscula Math. 45, no. 1 (2025), 27-38
https://doi.org/10.7494/OpMath.2025.45.1.27
Opuscula Mathematica
Monotonic properties of Kneser solutions of second order linear differential equations with delayed argument
Abstract. In this paper new monotonic properties of nonoscillatory solutions for second order linear functional differential equations with delayed argument \[y{''}(t)=p(t)y(\tau(t))\] have been established. New properties are used to introduce criteria for elimination of bounded nonoscillatory solutions for studied equations.
Keywords: second order, differential equations, delayed argument, monotonic properties, oscillation.
Mathematics Subject Classification: 34K11, 34C10.
- R.P. Agarwal, S.R. Grace, D. O'Regan, Oscillation Theory for Second Order Linear, Half-linear, Superlinear and Sublinear Dynamic Equations, Kluver Academic Publishers, Dordrecht 2002. https://doi.org/10.1007/978-94-017-2515-6
- R.P. Agarwal, C.H. Zhang, T. Li, Some remarks on oscillation of second order neutral differential equations, Appl. Math. Comput. 274 (2016), 178-181. https://doi.org/10.1016/j.amc.2015.10.089
- B. Baculíková, Oscillation of second-order nonlinear noncanonical differential equations with deviating argument, Appl. Math. Lett. 91 (2019), 68-75. https://doi.org/10.1016/j.aml.2018.11.021
- B. Baculíková, Oscillatory behavior of the second order noncanonical differential equation, Electron. J. Qual. Theory Differ. Equ. 89 (2019), 1-17. https://doi.org/10.14232/ejqtde.2019.1.89
- B. Baculíková, Oscillation and asymptotic properties of second order half-linear differential equations with mixed deviating arguments, Mathematics 9 (2021), 1-12. https://doi.org/10.3390/math9202552
- B. Baculíková, J. Džurina, Asymptotic properties of even-order functional differential equations with deviating argument, Carpathian J. Math. 40 (2024), 15-23. https://doi.org/10.37193/CJM.2024.01.02
- M. Bohner, S.R. Grace, I. Jadlovská, Oscillation criteria for second-order neutral delay differential equations, Electron. J. Qual. Theory Differ. Equ. 60 (2017), 1-12. https://doi.org/10.14232/ejqtde.2017.1.60
- G. Chatzarakis, I. Jadlovská, Improved oscillation results for second-order half-linear delay differential equations, Hacet. J. Math. Stat. 48, (2019). https://doi.org/10.15672/hjms.2017.522
- J. Džurina, Oscillation of second-order trinomial differential equations with retarded and advanced arguments, Appl. Math. Lett. 153 (2024), 1-8. https://doi.org/10.1016/j.aml.2024.109058
- I. Jadlovska, Oscillation criteria of Kneser-type for second-order half-linear advanced differential equations, Appl. Math. Lett. 106 (2020), 1-8. https://doi.org/10.1016/j.aml.2020.106354
- I. Jadlovská, J. Džurina, Kneser-type oscillation criteria for second-order half-linear delay differential equations, Appl. Math. Comput. 380, (2020), 1-15. https://doi.org/10.1016/j.amc.2020.125289
- I.T. Kiguradze, T.A. Chanturia, Asymptotic Properties of Solutions of Nonatunomous Ordinary Differential Equations, Kluwer Acad. Publ., Dordrecht, 1993. https://doi.org/10.1007/978-94-011-1808-8
- R. Koplatadze, T.A. Chanturia, On Oscillatory Properties of Differential Equations with Deviating Arguments, Tbilisi Univ. Press, Tbilisi, 1977.
- R. Koplatadze, G. Kvinkadze, I.P. Stavroulakis, Properties \(A\) and \(B\) of \(n\)-th order linear differential equations with deviating argument, Georgian Math. J. 6 (1999), 553-566. https://doi.org/10.1515/gmj.1999.553
- T. Kusano, On even order functional differential equations with advanced and retarded arguments, J. Differential Equations 45 (1982), 75-84. https://doi.org/10.1016/0022-0396(82)90055-9
- T. Kusano, Oscillation of even order linear functional differential equations with deviating arguments of mixed type, J. Math. Anal. Appl. 98 (1984), 341-347. https://doi.org/10.1016/0022-247x(84)90253-1
- T. Kusano, B.S. Lalli, On oscillation of half-linear functional differential equations with deviating arguments, Hiroshima Math. J. 24 (1994), 549-563. https://doi.org/10.32917/hmj/1206127926
- G. Laddas, V. Lakshmikantham, J.S. Papadakis, B.G. Zhang, Oscillation of higher-order retarded differential equations generated by retarded argument, Delay and Functional Differential Equations and Their Applications, Academic Press, New York, 1972, 219-231. https://doi.org/10.1016/b978-0-12-627250-5.50013-7
- T. Li, Y. Rogovchenko, Oscillation of second-order neutral differential equations, Math. Nachr. 288 (2015), 1150-1162. https://doi.org/10.1002/mana.201300029
- M. Naito, Oscillation Criteria for Second Order Ordinary Differential Equations, Canad. Math. Bull. 63 (2020), 276-286. https://doi.org/10.4153/s0008439519000262
- S. Tamilvanan, E. Thandapani, J. Džurina, Oscillation of second order nonlinear differential equation with sub-linear neutral term, Differ. Equ. Appl. 9 (2017), 1-7. https://doi.org/10.7153/dea-09-03
- Y. Wu, Y. Yu, J. Xiao, Oscillation of second order nonlinear neutral differential equations, Mathematics 10 (2022), 1-12. https://doi.org/10.3390/math10152739
- Blanka Baculíková
- Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Mathematics, Letná 9, 042 00 Košice, Slovakia
- Communicated by Josef Diblík.
- Received: 2024-06-26.
- Revised: 2024-09-12.
- Accepted: 2024-09-27.
- Published online: 2024-12-20.
