一类测度链上二阶三点边值问题对称解的存在性

Existence of symmetric solutions for a kind of second-order three-point boundary value problem on a measure chain

本文研究了一类测度链上二阶三点微分方程边值问题xΔΔ(t)+f(t,x(t))=0,t∈(0,1)∩T,x(0)=x(1),xΔ(0)-xΔ(1)=αx(ξ),这里,f:[0,1]×[0,∞)→[0,∞)是一连续函数,满足对称性条件f(t,x)=f(1-t,x),0,1,ξ∈T,0<ξ<1,α<1/(ξ-ξ2)。借助不动点指数性质的应用获得了3个对称正解的存在性。

This paper addresses the existence of symmetric positive solutions for the boundary value problem of a kind of second-order three-point differential equation on a measure chain,x△△ （t） ＋ f（t,x（t）） =0,t ∈ （0,1） ∩ T,x（0） =x（1）,x△ （0）-x△ （1） =ax（ξ）,Where f：[0,1] × [0,∞）→[0,∞） is continuous and satisfies f（t,x） =f（1-t,x）,0,1,ξ ∈ T,0 ＜ξ ＜ 1,α ＜ 1/（ξ-ξ2）.Existence of three symmetric positive solutions is acquired with fixed point index property.