Solvability of a Multi-Point Boundary Value Problem at Resonance

Let f: 0, 1] × R² → R be a function satisfying Caratheodory’s conditions and e(t) ∈ L¹0, 1]. Let η_i ∈ (0, 1), i = 1, …, k, with 0 s< η₁ < … < η_k < 1, be given. This paper is concerned with the problem of existence of a solution for the multi-point boundary value problem . Conditions for the existence of a solution for the above boundary value problem are given using Leray Schauder Continuation theorem.