Existence of solutions for a class of strongly coupled $p(x)-$ laplacian system

Abstract

We prove the existence of a non trivial weak solution for certain class of strongly coupled nonlinear system containing the ($p(x)-q(x))$ laplacian operators using as main argument the mountain pass Theorem of {\sc Ambrosetti-Rabinowitz}.

Keywords

• p$(x)-$Laplace operator
• Generalized Lebesgue-Sobolev spaces
• Strongly system
• Variational methods