Opuscula Math. 40, no. 5 (2020), 523-536
https://doi.org/10.7494/OpMath.2020.40.5.523

Opuscula Mathematica

# Oscillatory criteria via linearization of half-linear second order delay differential equations

Blanka Baculíková
Jozef Džurina

Abstract. In the paper, we study oscillation of the half-linear second order delay differential equations of the form $\left(r(t)(y'(t))^{\alpha}\right)'+p(t)y^{\alpha}(\tau(t))=0.$ We introduce new monotonic properties of its nonoscillatory solutions and use them for linearization of considered equation which leads to new oscillatory criteria. The presented results essentially improve existing ones.

Keywords: second order differential equations, delay, monotonic properties, linearization, oscillation.

Mathematics Subject Classification: 34K11, 34C10.

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• Blanka Baculíková (corresponding author)
• https://orcid.org/0000-0002-8689-6308
• Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Mathematics, Letná 9, 042 00 Košice, Slovakia
• Jozef Džurina
• https://orcid.org/0000-0002-6872-5695
• Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Mathematics, Letná 9, 042 00 Košice, Slovakia
• Communicated by Josef Diblík.
• Revised: 2020-09-11.
• Accepted: 2020-09-12.
• Published online: 2020-10-10.