Multiple solutions for a perturbed mixed boundary value problem involving the one-dimensional $p$-Laplacian

Abstract

The existence of three distinct weak solutions for a perturbed mixed boundary value problem involving the one-dimensional $p$-Laplacian operator is established under suitable assumptions on the nonlinear term. Our approach is based on recent variational methods for smooth functionals defined on reflexive Banach spaces.

Keywords

• multiple solutions
• perturbed mixed boundary value problem
• critical point theory
• variational methods