Existence Results for Quasilinear Degenerated Equations Via Strong Convergence of Truncations

Abstract

In this paper we study the existence of solutions for quasilinear degenerated elliptic operators A(u) + g (x, u, u) = f , where A is a Leray-Lions operator from W0 ,p (, w) into its dual, while g (x, s, ) is a nonlinear term which has 1 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 (, w ) or to L1 ().