Infinitely many solutions for systems of multi-point boundary value problems using variational methods

Abstract

In this paper, we obtain the existence of infinitely many classical solutions to the multi-point boundary value system $$ \begin{cases} -(\phi_{p_i}(u'_{i}))'=\lambda F_{u_{i}}(x,u_{1},\ldots,u_{n}),\qquad t\in (0,1),\\ \displaystyle \\ u_{i}(0)=\sum_{j=1}^m a_ju_i(x_j),\quad u_{i}(1)=\sum_{j=1}^m b_ju_i(x_j), \end{cases} \quad i=1,\ldots,n. $$ Our analysis is based on critical point theory.