Positive solutions of two-point boundary value problems for2n-order differential equations dependent on all derivatives

Abstract

In this work, we consider the higher-order differential equationsubject to one of the following multi-point boundary value conditions:orwhere f (t, x 0 , x 1 , . . . , x 2n−1 ) is continuous with f (t, x 0 , x 1 , . . . , x 2n−1 ) ≥ 0 for all t ∈ [0, 1] and (x 0 , x 1 , . . . , x 2n−1 ) ∈ R 2n . Sufficient conditions for the existence of at least one positive solution of the BVP (1) and (2) and BVP (1) and (3) are established, respectively. The emphasis in this work is on f depending on all higher-order derivatives. Examples are given to illustrate the main results.