Existence Of Solutions Of Second-order Ordinary Differential Equation Infinite-Point Boundary Value Problems

This paper is concerned with the infinite-point boundary value problems of second order ordinary differential equation(ODE) and some theorems related to the existence of nontrivial solutions of this problem is obtained.Whereα_i,β_i∈(0,∞),ξ_i∈(0,1),i∈Z⁺ satisfyξ₁＜ξ₂＜…＜ξ_n＜…,∑_i=1^∞α_i∑_i=1^∞β_iξ_i＞∑_i=1^∞β_i∑_i=1^∞α_iξ_i.f:[0,1]×R→[0,+∞)is continuous.