A multiplicity result for a perturbation of a symmetric dirichlet problem

Abstract

In this article we deal with the existence of at least three distinct weak solutions for the following Dirichlet problem

where

is a bounded open set with sufficiently smooth boundary

are Carthéodory functions with f(x, ·) odd for a.e. x ∈ Ω. Our main result assures that, for any neighborhood of zero

, there exist an open interval

and a positive real number ρ such that, for each λ ∈ J, the problem above has at least three weak solutions whose norms in

are less than ρ.

Keywords:

• Symmetric Dirichlet problem
• Weak solution
• Odd nonlinearity
• Mathematics Subject Classification (2000): 35J20