Uniqueness and existence results for a third-order nonlinear multi-point boundary value problem

被引：19

作者：

Lin, Xiaojie ^{[1
,2
]}

Du, Zengji ^{[1
]}

Liu, Wenbin ^{[2
]}

机构：

[1] Xuzhou Normal Univ, Sch Math Sci, Xuzhou 221116, Jiangsu, Peoples R China

[2] China Univ Min & Technol, Dept Math, Xuzhou 221008, Jiangsu, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 205卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Nonlinear boundary value problem; Existence and uniqueness; Upper and lower solutions; Leray-Schauder degree;

D O I：

10.1016/j.amc.2008.05.132

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper provides sufficient conditions for the existence and uniqueness of solutions to a nonlinear multi-point boundary value problem for third order differentia equation. The nonlinear term f in the differential equation under consideration may depend on second-order derivative. The emphasis here is the boundary conditions are nonlinear and this is where the main novelty of this work lies. By applying the upper and lower solutions method, as well as degree theory, the existence and uniqueness results of the problem are established. Some examples are given to demonstrate the main results. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：187 / 196

页数：10

共 17 条

[1]

Chang KW, 1984, NONLINEAR SINGULAR P

[2] Asymptotic solutions for a second-order differential equation with three-point boundary conditions [J].

Du, Zengji ;

Bai, Zhanbing .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (01) :469-473

[3] Singular perturbations for third-order nonlinear multi-point boundary value problem [J].

Du, ZJ ;

Ge, WG ;

Zhou, MG .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 218 (01) :69-90

[4] Multiple solutions for three-point boundary value problem with nonlinear terms depending on the first order derivative [J].

Du, ZJ ;

Xue, CY ;

Ge, WG .

ARCHIV DER MATHEMATIK, 2005, 84 (04) :341-349

[5] On a third-order multi-point boundary value problem at resonance [J].

Du, ZJ ;

Lin, XJ ;

Ge, WG .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 302 (01) :217-229

[6] Existence of solutions for a class of third-order nonlinear boundary value problems [J].

Du, ZJ ;

Ge, WG ;

Lin, XJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 294 (01) :104-112

[7]

Grossinho MD, 2001, NONLINEAR ANAL-THEOR, V47, P2407

[8] Existence result for a third-order ODE with nonlinear boundary conditions in presence of a sign-type Nagumo control [J].

Grossinho, MR ;

Minhós, FM ;

Santos, AI .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 309 (01) :271-283

[9] SOLVABILITY OF A 3-POINT NONLINEAR BOUNDARY-VALUE PROBLEM FOR A 2ND-ORDER ORDINARY DIFFERENTIAL-EQUATION [J].

GUPTA, CP .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 168 (02) :540-551

[10]

ILIN VA, 1987, DIFF EQUAT+, V23, P803

← 1 2 →