Positive solutions for second-order superlinear repulsive singular Neumann boundary value problems

被引：15

作者：

Chu, Jifeng ^{[1
]}

Lin, Xiaoning ^{[2
]}

Jiang, Daqing ^{[2
]}

O'Regan, Donal ^{[3
]}

Agarwal, Ravi P. ^{[4
]}

机构：

[1] Hohai Univ, Coll Sci, Nanjing 210098, Peoples R China

[2] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[3] Natl Univ Ireland, Dept Math, Galway, Ireland

[4] Florida Inst Technol, Dept Math Sci, Melbourne, FL 32901 USA

来源：

POSITIVITY | 2008年 / 12卷 / 03期

关键词：

superlinear; repulsive singular; Neumann boundary value problems; positive solutions; leray-Schauder alternative; fixed point theorem in cones;

D O I：

10.1007/s11117-007-2144-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we establish the multiplicity of positive solutions to second-order superlinear repulsive singular Neumann boundary value problems. It is proved that such a problem has at least two positive solutions under reasonable conditions. Our nonlinearity may be repulsive singular in its dependent variable and superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.

引用

页码：555 / 569

页数：15

共 17 条

[1] Optimal existence conditions for φ-Laplacian equations with upper and lower solutions in the reversed order [J].

Cabada, A ;

Habets, P ;

Pouso, RL .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 166 (02) :385-401

[2] A positive operator approach to the Neumann problem for a second order ordinary differential equation [J].

Cabada, A ;

Sanchez, L .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 204 (03) :774-785

[3] Monotone method for the Neumann problem with lower and upper solutions in the reverse order [J].

Cabada, A ;

Habets, P ;

Lois, S .

APPLIED MATHEMATICS AND COMPUTATION, 2001, 117 (01) :1-14

[4] Existence result for the problem (φ(u′))′=f(t,u,u′) with periodic and Neumann boundary conditions. [J].

Cabada, A ;

Pouso, RL .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (03) :1733-1742

[5] A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions [J].

Cherpion, M ;

De Coster, C ;

Habets, P .

APPLIED MATHEMATICS AND COMPUTATION, 2001, 123 (01) :75-91

[6] Positive solutions of Neumann problems with singularities [J].

Chu, Jifeng ;

Sun, Yigang ;

Chen, Hao .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 337 (02) :1267-1272

[7] Existence and uniqueness results for some nonlinear boundary value problems [J].

Dang, H ;

Oppenheimer, SF .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 198 (01) :35-48

[8]

Deimling K., 2010, NONLINEAR FUNCTIONAL, DOI DOI 10.1007/978-3-662-00547-7

[9] A Neumann problem at resonance with the nonlinearity restricted in one direction [J].

Dong, YJ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 51 (05) :739-747

[10] ON THE EXISTENCE OF POSITIVE SOLUTIONS OF ORDINARY DIFFERENTIAL-EQUATIONS [J].

ERBE, LH ;

WANG, HY .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 120 (03) :743-748

← 1 2 →