一类广义二阶常微分方程三点积分边值问题正解的存在性

Positive Solutions to a Generalized Second-order Three-point Integral Boundary Value Problem

该文运用了格林公式的性质和锥上不动点定理,建立了一个广义二阶常微分方程三点积分边值问题在超线性和次线性条件下至少有一个正解的存在性定理.同时给出了在这一边值条件下至少有两个正解存在的充分条件.

In this work, we focus on the existence of＇solutions for a class of nonlinear sec- ond-order three-point integral boundary value problem. Using the properties of the Green function and Krasnosel^kii fixed point theorem,we obtain that the boundary value problem has at least one positive solutions in the superlinear or sublinear case. Also, some sufficient conditions has been obtained that the problem has at least two positive solutions.