二阶微分方程积分边界问题多解的存在性

On the Existence of Multiple Positive Solutions for Second-order Differential Equations with Integral Boundary Value Problems

摘要

摘要:研究了一类含积分边界条件的二阶微分方程多个正解的存在性.首先, 利用锥上不动点定理及给定的假设条件证明了该类方程具有两个不同的非零解;其次, 利用Leggett-Williams不动点定理结合一定的假设条件得到了该类方程三个正解的存在性.

Abstract:The existence of multiple positive solutions for a class of second-order differential equations with integral boundary conditions is studied.First, by using the fixed point theorem on the cone and the given hypothesis conditions, it is proved that this class of equations have two different non-zero solutions;secondly, the existence of three positive solutions to this class of equation is proved by using the Leggett-Williams fixed point theorem in combination with certain assumed conditions.