ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

Subject Areas : International Journal of Mathematical Modelling & Computations

Nemat Nyamoradi ¹ (Iran, Islamic Republic of)
Mohsen Shekarbaigi ² (Iran, Islamic Republic of)

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2013-03-21

Keywords: Quasilinear elliptic system, Critical Hardy exponents, Singular weights, Energy functional, Variational method,

Abstract :

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