Existence of symmetric positive solutions for lidstone type integral boundary value problems

Abstract

This paper establishes the existence of even number of symmetric positive solutions for the even order differential equation (−1)n u (2n) (t) = f(t, u(t)), t ∈ (0, 1), satisfying Lidstone type integral boundary conditions of the form u (2i) (0) = u (2i) (1) = Z 1 0 ai+1(x)u (2i) (x)dx, for 0 ≤ i ≤ n − 1, where n ≥ 1, by applying Avery–Henderson fixed point theorem.