Quasilinear elliptic systems in R^N with multipower forcing terms depending on the gradient

In this paper we deal with non coercive elliptic multipower systems of divergence type, which include p-Laplacian type operators as well as mean curvature operators and whose right hand sides depend on the product of both components of the solution and on a gradient factor. We prove that any nonnegative nontrivial entire weak solution (non necessarily radial) is constant. For nontrivial solutions we intend that both components are nontrivial. The paper improves former results due to Clèment, Fleckinger, Mitidieri, de Thèlin and to Bidaut-Veron and Pohozaev, where no gradient terms are considered.