Existence of positive solutions for a class of second-order two-point boundary value problem

被引：2

作者：

Zhang, Guowei ^{[1
]}

Sun, Jingxian ^{[2
]}

Zhang, Tie

机构：

[1] Northeastern Univ, Dept Math, Shenyang 110004, Peoples R China

[2] Xuzhou Normal Univ, Dept Math, Xuzhou 221116, Peoples R China

来源：

POSITIVITY | 2008年 / 12卷 / 03期

基金：

中国国家自然科学基金;

关键词：

positive solution; cone; fixed point index;

D O I：

10.1007/s11117-007-2159-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By using different convex functionals to compute fixed point index, the existence of positive solutions for a class of second-order two-point boundary value problem {phi ''(t) + h(t) f(phi(t)) = 0, 0 < t < 1, alpha phi(0) - beta phi'(0) = 0, gamma phi(1) + delta phi'(1) = 0, is obtained under some conditions of growth, where alpha, beta, gamma, delta, >= 0, rho = alpha gamma + gamma beta + delta alpha > 0, and h(t) is allowed to be singular at t = 0 and t = 1.

引用

页码：547 / 554

页数：8

共 12 条

[1] Fixed point theorem of cone expansion and compression of functional type [J].

Anderson, DR ;

Avery, RI .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2002, 8 (11) :1073-1083

[2] Eigenvalue criteria for existence of positive solutions to nonlinear boundary value problems [J].

Erbe, L .

MATHEMATICAL AND COMPUTER MODELLING, 2000, 32 (5-6) :529-539

[3] Positive solutions for singular nonlinear boundary value problems [J].

Erbe, LH ;

Mathsen, RM .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 46 (07) :979-986

[4] 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

[5]

Guo D., 1988, NONLINEAR PROBLEMS A

[6] Positive solutions for nonlinear eigenvalue problems [J].

Henderson, J ;

Wang, HY .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 208 (01) :252-259

[7]

MA RY, 1998, ACTA MATH SINICA, V41, P1225

[8] Compression-expansion fixed point theorem in two norms and applications [J].

O'Regan, D ;

Precup, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 309 (02) :383-391

[9] The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the p-Laplacian operator [J].

Su, Hua ;

Wei, Zhongli ;

Xu, Fuyi .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (01) :319-332

[10] Positive solvability of systems of nonlinear Hammerstein integral equations [J].

Yang, ZL ;

O'Regan, D .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 311 (02) :600-614

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