POSITIVE SOLUTIONS OF A NONLINEAR STURM-LIOUVILLE BOUNDARY-VALUE PROBLEM

被引：0

作者：

Cerda, Patricio ^{[1
]}

Ubilla, Pedro ^{[1
]}

机构：

[1] Univ Santiago Chile, Fac Ciencias, Dept Matemat & Ciencia Computac, Santiago, Chile

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2009年 / 52卷

关键词：

Sturm-Liouville problems; positive solutions; fixed points; topological degree; SUPERLINEAR NONLINEARITIES; EXISTENCE; 2ND-ORDER; EQUATIONS;

D O I：

10.1017/S0013091507000120

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the existence of positive solutions of the Sturm-Liouville problem - (p(s, u)u')' = (q) over cap (s)u(p)h(s, u, u') in (0, 1), u(0) = 0 = u(1), where p(s, u) = 1/(a(s) + cg(u)). We assume g and (q) over cap to be non-negative, continuous functions, a(s) is a positive continuous function, c >= 0, p > 1, and the function h is sub-quadratic with respect to u'. We combine a priori estimates with a fixed-point result of Krasnosel'skii to obtain the existence of a positive solution.

引用

页码：561 / 568

页数：8

共 17 条

[1] The existence of positive solutions for the Sturm-Liouville boundary value problems [J].

Agarwal, RP ;

Hong, HL ;

Yeh, CC .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 35 (09) :89-96

[2] Existence results for superlinear semipositone BVP's [J].

Anuradha, V ;

Hai, DD ;

Shivaji, R .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (03) :757-763

[3]

Brezis H., 1977, Commun. Partial Differ. Equ., V2, P601, DOI 10.1080/03605307708820041

[4] Existence theory for functional p-Laplacian equations with variable exponents [J].

Cabada, A ;

Pouso, RL .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (02) :557-572

[5] EXISTENCE OF SOLUTIONS FOR SOME NONLINEAR SINGULAR BOUNDARY-VALUE-PROBLEMS [J].

DUNNINGER, DR ;

KURTZ, JC .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1986, 115 (02) :396-405

[6] A PRIORI BOUNDS AND EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR NONLINEAR BOUNDARY-VALUE-PROBLEMS [J].

DUNNINGER, DR ;

KURTZ, JC .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1986, 17 (03) :595-609

[7]

Garner J. B., 1988, Applicable Analysis, V30, P101, DOI 10.1080/00036818808839795

[8]

Krasnoselskii M. A, 1964, Positive Solutions of Operator Equations

[9] Multiple positive solutions of semi-positone Sturm-Liouville boundary value problems [J].

Lan, KQ .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2006, 38 :283-293

[10] On the existence and nonexistence of positive solutions for nonlinear Sturm-Liouville boundary value problems [J].

Li, YX .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 304 (01) :74-86

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