Multiple solutions for systems of multi-point boundary value problems

Abstract

In this paper, we establish the existence of at least three solutions of the multi-point boundary value system $\left\{\begin{array}{ll} -(\phi_{p_i}(u'_{i}))'=\lambda F_{u_{i}}(x,u_{1},\ldots,u_{n}),\ t\in(0,1),\\ u_{i}(0)=\sum_{j=1}^m a_ju_i(x_j),\ u_{i}(1)=\sum_{j=1}^m b_ju_i(x_j), \end{array}\right. i=1,\ldots,n.$ The approaches used are based on variational methods and critical point theory.