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.
- Received: 2020-06-11.
- Revised: 2020-09-11.
- Accepted: 2020-09-12.
- Published online: 2020-10-10.
