Third-order boundary value problems with sign-changing solutions

被引：53

作者：

Hopkins, Britney ^{[1
]}

Kosmatov, Nickolai ^{[1
]}

机构：

[1] Univ Arkansas, Dept Math & Stat, Little Rock, AR 72204 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 67卷 / 01期

关键词：

a priori estimate; Caratheodory; Leray-Schauder Continuation Principle;

D O I：

10.1016/j.na.2006.05.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the third-order nonlinear differential equation u''' (t) = f (t, u (t), u'(t), u" (t)), a.e. t is an element of (0, 1), satisfying u(0) = u'(0) = u"(1) = 0 and u(0) = u'(1) = u"(1) = 0, where f : [0, 1] x R-3 -> R is L-p-Caratheodory, 1 <= p < infinity. We obtain the existence of at least one positive solution using the Leray-Schauder Continuation Principle for each set of boundary conditions by separately considering the cases p > 1 and p = 1. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：126 / 137

页数：12

共 16 条

[1] Green's function for a third-order generalized right focal problem [J].

Anderson, DR .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 288 (01) :1-14

[2] Positive solutions for singular non-linear third-order periodic boundary value problems [J].

Chu, JF ;

Zhou, ZC .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (07) :1528-1542

[3] A Dirichelet-Neumann m-point BVP with a p-Laplacian-like operator [J].

García-Huidobro, M ;

Gupta, CP ;

Mandsevich, R .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 62 (06) :1067-1089

[4]

Graef JR, 2006, DYNAM SYST APPL, V15, P97

[5]

Gupta C., 2001, ELECT J DIFFER EQU C, V7, P47

[6] A priori estimates for the existence of a solution for a multi-point boundary value problem [J].

Gupta, CP ;

Trofimchuk, S .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2000, 5 (04) :351-365

[7]

Gupta CP, 2004, PROCEEDINGS OF DYNAMIC SYSTEMS AND APPLICATIONS, VOL 4, P439

[8] EXISTENCE AND UNIQUENESS THEOREMS FOR A 3RD-ORDER 3-POINT BOUNDARY-VALUE PROBLEM [J].

GUPTA, CP ;

LAKSHMIKANTHAM, V .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1991, 16 (11) :949-957

[9]

GUPTA CP, 2001, DYNAM SYSTEMS APPL, V3, P249

[10] Existence of solutions for third-order boundary value problems on a time scale [J].

Henderson, J ;

Yin, WKC .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (6-9) :1101-1111

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