Quasilinear elliptic systems with critical Sobolev exponents in [formula omitted

Abstract

We study here a class of quasilinear elliptic systems involving the p -Laplacian operator; the right hand sides of systems are closely related to the critical Sobolev exponents. Under some additional assumptions on the nonlinearities, the corresponding functional verifies the Palais–Smale condition ( P S ) c for c belonging to a specified range. So, we can use the Mountain Pass Theorem to prove the existence of at least one nontrivial solution.