EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC SYSTEM WITH NONLINEAR BOUNDARY.

Abstract

In this paper, we establish some results on the existence of multiple nontrivial solutions for a class of p(x)Laplacian elliptic systems. Our approach relies on the variable exponent theory of generalized Lebesgue–Sobolev spaces, combined with adequate variational methods and a variant of the Mountain Pass lemma.