Existence of multiple solutions to a two-point boundary value system via variational method

Abstract

In this paper, we prove the existence of an open interval $mathrm{]}{lambda }^{mathrm{'}},{lambda }^{mathrm{''}}mathrm{[}$ for each $lambda $ of which a class of two-point boundary value equations depending on $lambda $ admits at least three solutions. Our main tool is a three critical points theorem of Averna and Bonanno.