具非线性中立项的二阶延迟微分方程的Philos型准则

Abstract

Abstract:

We study the oscillatory behavior of Emden-Fowler-type differential equations with a nonlinear neutral term

$\{a(t)|[x(t)+p(t)x^\alpha(\tau(t))]'|^{\beta-1}[x(t)+p(t)x^\alpha(\tau(t))]'\}'+q(t)f(|x(\delta(t))|^{\gamma-1}x(\delta(t)))=0, t\geq t_0$

in this article. By using the generalized Riccati transformation, and Bernoulli inequality, Yang inequality and integral averaging technique, we establish some new oscillation criterions for the equations. The illustrative examples are provided to show that our results obtained extend and improve those reported in the literature, and have practicability and maneuverability.

Key words: Oscillation, Emden-Fowle differential equation, Nonlinear neutral, Riccati transformation

CLC Number:

O175.1

Jimeng Li,Jiashan Yang. Philos-Type Criteria for Second-Order Delay Differential Equations with Nonlinear Neutral Term[J].Acta mathematica scientia,Series A, 2020, 40(1): 169-186.

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References 18

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Philos-Type Criteria for Second-Order Delay Differential Equations with Nonlinear Neutral Term

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