ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variational method, we obtain the existence non-trivialweek solution for the system