Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation-Reference-Cited by-同舟云学术

Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation

Published:2011 Issue: Volume:2011 Page:1-23
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Liu Zeqing¹,Chen Lin¹,Kang Shin Min²,Cho Sun Young³

Affiliation:

1. Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China

2. Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

3. Department of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of Korea

Abstract

The aim of this paper is to study the solvability of a third-order nonlinear neutral delay differential equation of the form{α(t)[β(t)(x(t)+p(t)x(t−τ))′]′}′+f(t,x(σ1(t)),x(σ2(t)),…,x(σn(t)))=0,t≥t0. By using the Krasnoselskii's fixed point theorem and the Schauder's fixed point theorem, we demonstrate the existence of uncountably many bounded nonoscillatory solutions for the above differential equation. Several nontrivial examples are given to illustrate our results.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2011/693890.pdf

Reference12 articles.

1. Existence of Positive Solutions of a Singular Initial Problem for a Nonlinear System of Differential Equations

2. Existence of positive solutions of delay differential equations

3. Oscillation/Nonoscillation Criteria for Linear Second Order Differential Equations

4. Oscillation and Nonoscillation for Second Order Linear Differential Equations

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