Abstract:

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,  xΔΔ(t)+f(t,x(t))=0,t∈(0,1)∩T,x(0)=x(1),xΔ(0)-xΔ(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.

Key words: boundary value problem, symmetric solution, measure chains, fixed point index