一类Sturm-Liouville边值问题正解的存在性

J4 ›› 2010, Vol. 45 ›› Issue (2): 84-89.

一类Sturm-Liouville边值问题正解的存在性

杨景保

亳州师范高等专科学校理科系, 安徽蒙城 233500

收稿日期:2008-12-23 出版日期:2010-02-16 发布日期:2010-03-27
作者简介:杨景保(1968-)，男，硕士，讲师，研究方向为非线性泛函数分析与微分方程.Email:jbyang1@126.com
基金资助:
亳州师范高等专科学校科研资助项目(BSKY0805)；安徽省自然科学研究项目(KJ2009B093)

Existence of positive solutions for a class of Sturm-Liouville boundary value problems

Department of Sciences, Bozhou Teachers College, Mengcheng 233500, Anhui, China

Received:2008-12-23 Online:2010-02-16 Published:2010-03-27

摘要/Abstract

摘要：

研究了一类含有一维p-Laplacian算子的Sturm-Liouville边值问题的正解的存在性, 非线性项含有未知函数的一阶导数。通过应用范数形式的锥拉伸与压缩不动点定理, 得到了正解存在的几个充分条件。

关键词: p-Laplacian算子; Sturm-Liouville边值问题; 锥拉伸与压缩不动点定理; 正解

Abstract:

The existence of positive solutions is investigated for a class ofSturm-Liouville boundary value problems with a one-dimensional p-Laplacian operator though the nonlinear term contained first derivative of an unknown function.Byapplying the fixed-point theorem of cone expansion and compression of norm type, the several sufficient conditions of existence of positive solutions are obtained.

Key words: p-Laplacian operator; Sturm-Liouville boundary value problems; fixed-point theorem of cone expansion and compression; positive solution

杨景保. 一类Sturm-Liouville边值问题正解的存在性[J]. J4, 2010, 45(2): 84-89.

YANG Jing-Bao. Existence of positive solutions for a class of Sturm-Liouville boundary value problems[J]. J4, 2010, 45(2): 84-89.

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