烟台大学学报（自然科学与工程版）2001，Vol.14Issue(2)：79-86,8.
非线性Dirichlet边值问题的两正解存在性
The Existence of Two Positive Solutions for a Nonlinear Dirichlet Boundary Value Problem
摘要
Abstract
The existence of positive solutions has been discussed for the nonlinear boundary value problem y″+f(y)=0,y(0)=0, and y(1)=b＞0, where f is a locally Lipschitz continuous,f(0)≥0 and may change signs. The main result of this paper is as follows: If f satisfies a superlinear condition at ＋∞ and there a nonnegative supersolution β with β(1)＞0 exists, then there is a positive number B such that the problem at least two positive solutions for b＜B, at least one for b=B, and none for b＞B. The approach is based on the Leray-Schauder degree arguments and the method of sub-and supersolutions.关键词
边值问题/正解/存在性/上下解/拓扑度Key words
boundary value problem/positive solution/existence/sub-and supersolution/topological degree分类
数理科学引用本文复制引用
程建纲..非线性Dirichlet边值问题的两正解存在性[J].烟台大学学报（自然科学与工程版）,2001,14(2):79-86,8.基金项目
国家自然科学基金资助项目(10071066). （10071066）
