Science and Education Publishing International Journal of Partial Differential Equations and Applications 2 5 2014 11 16 Weak Solutions for a Class of (p,q) Laplacian quasilinear Elliptic System with Different Weights 86 90 EN Tahar Bouali Department of Mathematics, University Tebessa, Algeria Rafik Guefaifiai IJPDEA2014251 10.12691/ijpdea-2-5-1 2014 03 30 2014 11 09 2014 11 16 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