Oscillation of fourth-order neutral differential equations with p-Laplacian like operators

Tongxing Li,Jozef Džurina,Blanka Baculíková,Chenghui Zhang

doi:10.1186/1687-2770-2014-56

Abstract

We study oscillatory behavior of a class of fourth-order neutral differential equations with a p-Laplacian like operator using the Riccati transformation and integral averaging technique. A Kamenev-type oscillation criterion is presented assuming that the noncanonical case is satisfied. This new theorem complements and improves a number of results reported in the literature. An illustrative example is provided. MSC:34C10, 34K11.

Highlights

1 Introduction In this paper, we are concerned with oscillation of a class of fourth-order neutral differential equations with a p-Laplacian like operator l r(t) z (t) p– z (t) + qi(t) x τi(t) p– x τi(t) =, ( . )
Throughout, we assume that p > is a constant, I := [t, ∞), r ∈ C (I, (, ∞)), r (t) ≥, a, σ, qi, τi ∈ C(I, R), ≤ a(t) , and limt→∞ τ (t) = ∞
Oscillation theorem established in this paper for equation ( . ) complements, on one hand, results reported by Baculíková and Džurina [ ], Karpuz [ ], and Li et al [ ] because we use assumption ( . ) rather than ( . ) and, on the other hand, those by Li et al [ ] and Zhang et al [, – ] since our theorem can be applied to the case where a(t) =

Summary

Open Access

Oscillation of fourth-order neutral differential equations with p-Laplacian like operators. Tongxing Li1*, Blanka Baculíková[2], Jozef Džurina[2] and Chenghui Zhang[3] This paper is dedicated to Professor Ivan Kiguradze

Introduction

This yields t

Now set