Opuscula Mathematica
Opuscula Math. 39, no. 4 (2019), 483-495

Oscillatory results for second-order noncanonical delay differential equations

Jozef Džurina
Irena Jadlovská
Ioannis P. Stavroulakis
Abstract. The main purpose of this paper is to improve recent oscillation results for the second-order half-linear delay differential equation \[\left(r(t)\left(y'(t)\right)^\gamma\right)'+q(t)y^\gamma(\tau(t))= 0, \quad t\geq t_0,\] under the condition \[\int_{t_0}^{\infty}\frac{\text{d} t}{r^{1/\gamma}(t)} \lt \infty.\] Our approach is essentially based on establishing sharper estimates for positive solutions of the studied equation than those used in known works. Two examples illustrating the results are given.
Keywords: linear differential equation, delay, second-order, noncanonical, oscillation.
Mathematics Subject Classification: 34C10, 34K11.
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About the authors ▼
Jozef Džurina
https://orcid.org/0000-0002-6872-5695
Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Mathematics and Theoretical Informatics, B. Němcovej 32, 042 00 Košice, Slovakia
Irena Jadlovská
https://orcid.org/0000-0003-4649-5611
Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Mathematics and Theoretical Informatics, B. Němcovej 32, 042 00 Košice, Slovakia
Ioannis P. Stavroulakis
https://orcid.org/0000-0002-4810-0540
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece; Al-Farabi Kazakh National University, Faculty of Mathematics and Mechanics, Almaty, 050040 Kazakhstan
About the article ▼
Communicated by Josef Diblík.
Received: 2019-01-24.
Revised: 2019-03-01.
Accepted: 2019-03-01.
Published online: 2019-05-23.
Cite this article as ▼
Jozef Džurina, Irena Jadlovská, Ioannis P. Stavroulakis, Oscillatory results for second-order noncanonical delay differential equations, Opuscula Math. 39, no. 4 (2019), 483-495, https://doi.org/10.7494/OpMath.2019.39.4.483.
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