  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.
