Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville type

Abstract

In this work, we establish the existence of two intervals for a parameter $lambda$ for which a two-point boundary-value problem of fourth-order Sturm-Liouville type admits three weak solutions whose norms are uniformly bounded with respect to $lambda$. Employing two three critical point theorems, existence of at least three weak solutions is ensured. This approach is based on variational methods and critical point theory.

Keywords

• Fourth-order Sturm-Liouville problem
• critical point
• multiplicity of solutions