eng Science and Education Publishing International Journal of Partial Differential Equations and Applications 2014-11-16 2 5 86 90 10.12691/ijpdea-2-5-1 IJPDEA2014251 article Weak Solutions for a Class of (p,q) Laplacian quasilinear Elliptic System with Different Weights Tahar Bouali boualitahar@yahoo.fr 1 Rafik Guefaifiai 1 Department of Mathematics, University Tebessa, Algeria Using variational methods, we study the existence of weak solutions for the degenerate quasilinear elliptic system where is a smooth bounded domain, stands for the gradient of -function the weights are allowed to vanish somewhere, the primitive is intimately related to the first eigenvalue of a corresponding quasilinear system http://pubs.sciepub.com/ijpdea/2/5/1/ijpdea-2-5-1.pdf quasilinear elliptic system Palais-Smale condition mountain pass theorem existence