一类二阶泛函微分方程正解的存在性

Existence of positive solutions for a class of second order functional differential equations

研究了Banach空间中二阶泛函微分方程四点边值问题正解的存在性。在-1<ω≤0及-r<ω≤0两种情形下,通过在Banach空间中构造一个合适的锥,并在锥中定义一个正算子,利用锥上的不动点定理,证明了该问题正解的存在性。最后,作为主要结果的应用,建立了两个具体的泛函微分方程多重正解的存在性结果。

The existence of positive solutions for four point second order functional differential equations in Banach space is studied.In both case-1<ω≤0 and-r<ω≤0,by constructing an appropriate cone in the Banach space and defining a positive operator in the cone,using the Krasnoselskii fixed point theorem on cones,the existence of positive solution to the problem is proved.Finally,as an application of the main results,the existence of multiple positive solutions of two specific functional differential equations is established.