Quasilinear elliptic systems with critical Sobolev exponents in RN

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 (PS)(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. (c) 2006 Elsevier Ltd. All rights reserved.