一类非局部边值问题正解的存在性

The Existence of Positive Solutions for a Nonlocal Boundary Value Problem

摘要:

考虑非线性非局部边值问题

其中边值条件 ， ；A，B是有界变差函数； ， ；非线性项 是连续的且允许变号的。本文根据两个锥上的不动点定理，讨论得到以上问题至少存在两个正解。并且利用三解定理，讨论得到以上问题至少存在三个正解。

Abstract: This paper discusses the boundary value problem with nonlocal integral boundary conditions where , ; A and B are functions of bounded variation; , ; the nonlinearity is continuous and is allowed to change sign. According to the fixed point theorem in double cones, we obtain that there exists at least two positive solutions. And according to three-solution theorem, we obtain that there exists at least three positive solutions.

文章引用：朱应丽, 于秀洁. 一类非局部边值问题正解的存在性[J]. 应用数学进展, 2018, 7(8): 1085-1094. https://doi.org/10.12677/AAM.2018.78126

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