Abstract
In this paper, by using subsuper solutions method, we study the existence of weak positive solutions for a new class of (p, q) Laplacian nonlinear elliptic system in bounded domains, when a(x), b(x), alpha(x), and ss(x) are sign-changing functions that maybe negative near the boundary, without assuming sign conditions on f(0), g(0), h(0), and gamma(0).