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

John R. Graef, Shapour Heidarkhani, Lingju Kong

Abstract


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

Keywords


Infinitely many solutions; multi-point boundary value problems; multiplicity results; critical point theory

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