Opuscula Math. 39, no. 4 (2019), 483-495
https://doi.org/10.7494/OpMath.2019.39.4.483

 
Opuscula Mathematica

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.

Full text (pdf)

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  • Jozef Džurina
  • ORCID iD 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
  • ORCID iD 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
  • ORCID iD 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
  • Communicated by Josef Diblík.
  • Received: 2019-01-24.
  • Revised: 2019-03-01.
  • Accepted: 2019-03-01.
  • Published online: 2019-05-23.
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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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