Opuscula Math. 42, no. 5 (2022), 659-671
https://doi.org/10.7494/OpMath.2022.42.5.659
Opuscula Mathematica
Properties of even order linear functional differential equations with deviating arguments of mixed type
Abstract. This paper is concerned with oscillatory behavior of linear functional differential equations of the type \[y^{(n)}(t)=p(t)y(\tau(t))\] with mixed deviating arguments which means that its both delayed and advanced parts are unbounded subset of \((0,\infty)\). Our attention is oriented to the Euler type of equation, i.e. when \(p(t)\sim a/t^n.\)
Keywords: higher order differential equations, mixed argument, monotonic properties, oscillation.
Mathematics Subject Classification: 34K11, 34C10.
- B. Baculikova, 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. Baculikova, Oscillatory behavior of the second order noncanonical differential equation, Electron. J. Qual. Theory Differ. Equ. 89 (2019), 1-11. https://doi.org/10.14232/ejqtde.2019.1.89
- B. Baculikova, Oscillation and asymptotic properties of second order half-linear differential equations with mixed deviating arguments, Mathematics 2021, 9(20), 2552. https://doi.org/10.3390/math9202552
- B. Baculikova, Oscillation of even order linear functional differential equations with mixed deviating arguments, Opuscula Math. 42 (2022), no. 4, 549-560. https://doi.org/10.7494/OpMath.2022.42.4.549
- 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), no. 6, 553-566. https://doi.org/10.1515/GMJ.1999.553
- R. Koplatadze, T.A. Chanturia, On Oscillatory Properties of Differential Equations with Deviating Arguments, Tbilisi Univ. Press, Tbilisi, 1977.
- T. Kusano, On even order functional differential equations with advanced and retarded arguments, J. Differential Equations 45 (1982), no. 1, 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
- G. Laddas, V. Lakshmikantham, J.S. Papadakis, Oscillation of higher-order retarded differential equations generated by retarded argument, Delay and functional differential equations and their applications (Proc. Conf., Park City, Utah, 1972), Academic Press, New York, 1972, 219-231. https://doi.org/10.1016/B978-0-12-627250-5.50013-7
- Jozef Dzurina
https://orcid.org/0000-0002-6872-5695- Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia
- Communicated by Josef Diblík.
- Received: 2022-06-08.
- Revised: 2022-08-14.
- Accepted: 2022-08-22.
- Published online: 2022-09-08.
