Oscillation results for second-order nonlinear neutral differential equations

Tongxing Li,Yuriy V Rogovchenko,Chenghui Zhang

doi:10.1186/1687-1847-2013-336

Abstract

Abstract We obtain several oscillation criteria for a class of second-order nonlinear neutral differential equations. New theorems extend a number of related results reported in the literature and can be used in cases where known theorems fail to apply. Two illustrative examples are provided. MSC:34K11.

Highlights

1 Introduction In this paper, we are concerned with the oscillation of a class of nonlinear second-order neutral differential equations r(t) x(t) + p(t)x(t – τ ) γ + q(t)f x(t), x σ (t) =, ( )
Many papers deal with the oscillation of neutral differential equations which are often encountered in applied problems in science and technology; see, for instance, Hale [ ]
4 Conclusions Most oscillation results reported in the literature for neutral differential equation ( ) and its particular cases have been obtained under the assumption ( ) which significantly simplifies the analysis of the behavior of z(t) = x(t) + p(t)x(t – τ ) for a nonoscillatory solution x(t) of ( )

Summary

Introduction

1 Introduction In this paper, we are concerned with the oscillation of a class of nonlinear second-order neutral differential equations r(t) x(t) + p(t)x(t – τ ) γ + q(t)f x(t), x σ (t) = , ( ) By a solution of equation ( ) we mean a continuous function x(t) defined on an interval [tx, +∞) such that r(t)((x(t) + p(t)x(t – τ )) )γ is continuously differentiable and x(t) satisfies ( ) for t ≥ tx. Many papers deal with the oscillation of neutral differential equations which are often encountered in applied problems in science and technology; see, for instance, Hale [ ].

Results

Conclusion