Some Multiplicity Results to the Existence of Three Solutions for a Dirichlet Boundary Value Problem Involving the p-Laplacian

Abstract

In this paper we prove the existence of two intervals of positive real parameters λ for a Dirichlet boundary value problem involving the p-Laplacian which admit three weak solutions, whose norms are uniformly bounded with respect to λ belonging to one of the two intervals. Our main tool is a three critical points theorem due to G. Bonanno [A critical points theorem and nonlinear differential problems, J. Global Optim., 28:249–258, 2004].

Keywords:

• three solutions
• critical point
• variational methods
• multiplicity results
• Dirichlet problem

AMS Sub ject Classification:

• 35J20
• 34A15