Quasilinear elliptic systems with critical Sobolev exponents in RNRN

We study here a class of quasilinear elliptic systems involving the pp-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(PS)c for cc belonging to a specified range. So, we can use the Mountain Pass Theorem to prove the existence of at least one nontrivial solution.