一类奇异次线性Sturm Liouville 边值问题

J4 ›› 2009, Vol. 44 ›› Issue (10): 36-38.

一类奇异次线性Sturm Liouville 边值问题

姚庆六

南京财经大学应用数学系, 江苏南京 210003

收稿日期:2009-03-10 出版日期:2009-10-16 发布日期:2009-12-07
作者简介:姚庆六(1946),男，教授，研究方向为非线性常微分方程.Email:yaoqingliu2002@hotmail.com
基金资助:
国家自然科学基金资助项目(10871059)

A class of singular sublinear Sturm-Liouville boundary value problems

TAO Qiang-Liu

Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, Jiangsu, China

Received:2009-03-10 Online:2009-10-16 Published:2009-12-07

摘要/Abstract

摘要：

研究了一类次线性Sturm-Liouville边值问题的正解, 其中允许非线性项f(t,u)在t=0, t=1和u=0处奇异.主要工具是相关线性问题的Green函数及相应的Hammerstein积分方程。通过考察非线性项在u=0和u=+∞处的增长特性并且利用锥上的Guo-Krasnosel'skii不动点定理证明了一个新的存在定理。

关键词: 奇异常微分方程; Sturm-Liouville 边值问题; 正解; 存在定理

Abstract:

The positive solution is studied for a class of sublinear Sturm-Liouville boundary value problems, where the nonlinear term f(t,u) is allowed to be singular at t=0, t=1and u=0.The main tools are the Green function of the related linear problem and the corresponding Hammerstein integral equation. By nsidering the growth features of the nonlinear term at u=0 and u=+∞,and applying the Guo-Krasnosel'skii fixed point theorem on a cone, a new existence theorem is proved

Key words: singular ordinary differential equation; Sturm-Liouville boundary value problem; positive solution; existence theorem

中图分类号:

O175.8

姚庆六. 一类奇异次线性Sturm Liouville 边值问题[J]. J4, 2009, 44(10): 36-38.

TAO Qiang-Liu. A class of singular sublinear Sturm-Liouville boundary value problems[J]. J4, 2009, 44(10): 36-38.

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