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

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

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,...

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Main Authors: Zeqing Liu, Lin Chen, Shin Min Kang, Sun Young Cho
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/693890
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spelling doaj-43ac1b93943a40debe15daff9c44a6002020-11-24T23:29:26ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/693890693890Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential EquationZeqing Liu0Lin Chen1Shin Min Kang2Sun Young Cho3Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaDepartment of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaDepartment of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of KoreaDepartment of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of KoreaThe 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.http://dx.doi.org/10.1155/2011/693890
collection DOAJ
language English
format Article
sources DOAJ
author Zeqing Liu
Lin Chen
Shin Min Kang
Sun Young Cho
spellingShingle Zeqing Liu
Lin Chen
Shin Min Kang
Sun Young Cho
Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation
Abstract and Applied Analysis
author_facet Zeqing Liu
Lin Chen
Shin Min Kang
Sun Young Cho
author_sort Zeqing Liu
title Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation
title_short Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation
title_full Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation
title_fullStr Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation
title_full_unstemmed Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation
title_sort existence of nonoscillatory solutions for a third-order nonlinear neutral delay differential equation
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2011-01-01
description 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.
url http://dx.doi.org/10.1155/2011/693890
work_keys_str_mv AT zeqingliu existenceofnonoscillatorysolutionsforathirdordernonlinearneutraldelaydifferentialequation
AT linchen existenceofnonoscillatorysolutionsforathirdordernonlinearneutraldelaydifferentialequation
AT shinminkang existenceofnonoscillatorysolutionsforathirdordernonlinearneutraldelaydifferentialequation
AT sunyoungcho existenceofnonoscillatorysolutionsforathirdordernonlinearneutraldelaydifferentialequation
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