二阶四点共振边值问题多解的存在性

Existence and Multiplicity of Solutions for Four-Point Boundary Value Problems at Resonance

本文考虑二阶四点共振边值问题x″(t)=f(t,x(t),x′(t)),0＜t＜1,x(0)= ax(ξ),x(1)=bx(η)．通过建立上下解方法,应用Mawhin重合度理论,获得了一些多解性结果．

In this paper,we deal with the second-order four-point boundary value problem.By applying the coincidence degree theory,the method of lower and upper solutions is established.Then some existence theorems for BVPs at resonance are proved.