Existence and nonexistence of solutions to nonlinear gradient elliptic systems involving (p(x),q(x))-Laplacian operators

Abstract

In this article, we establish the existence of nontrivial solutions by employing the fibering method introduced by Pohozaev. We also generalize the well-known Pohozaev and Pucci-Serrin identities to a (p(x),q(x))-Laplacian system. A nonexistence result for a such system is then proved.

Keywords

• Fibering method
• p(x)-Laplacian
• Generalized Pohozeav identity
• Pucci-Serrin identity