EXISTENCE OF ONE WEAK SOLUTION FOR ELLIPTIC EQUATIONS INVOLVING A GENERAL OPERATOR IN DIVERGENCE FORM

Abstract

In this paper, we establish the existence of at least two distinct weak solutions for a class of elliptic equations involving a general operator in divergence form, subject to Dirichlet boundary conditions in a smooth bounded domain in R N . A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least two distinct non-trivial weak solutions.