A generalized multi-point boundary value problem for second order ordinary differential equations

摘要

Let f: [0,1] × R2 → R be a function satisfying Caratheodory's conditions and e(t) ∈ L1[0,1]. Let ξi, τj ∈ (0,1), ai, bj ∈ R, i = 1, 2,…, m − 2, j = 1, 2,…, n−2, 0 < ξ1 < ξ2 < … < ξm−2 < 1, 0 < τ1 < τ2 < … < τn−2 < 1 be given. This paper is concerned with the problem of existence of a solution for the generalized multi-point boundary value problems ξ″(t)=f(t, ξ(t), ξ′(t)) + e(t), 0