Existence Results for Quasilinear Degenerated Equations Via Strong Convergence of Truncations

In this paper we study the existence of solutions for quasilinear degenerated elliptic operators A(u) + g(x,u,ru) = f , where A is a Leray-Lions operator from W 1,p 0 ( ,w) into its dual, while g(x,s, ) is a nonlinear term which has a growth condition with respect to and no growth with respect to s, but it satisfies a sign condition on s. The right hand side f is assumed to belong either to W 1,p 0 ( ,w ) or to L 1 ().