Solvability of a sixth-order boundary value problem with multi-point and multi-term integral boundary conditions

Abstract

This paper aims to investigate the existence and uniqueness of solutions for a sixth order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii-Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via H\"{o}lder and Minkowski inequalities and Rus's theorem. Finally, two examples are included to show the applicability of our main results.