Quasilinear degenerated equations with L1L^1 datum and without coercivity in perturbation terms

In this paper we study the existence of solutions for the generated boundary value problem, with initial datum being an element of $L^1(\Omega)+W^{-1, p'}(\Omega, w^{*})$ $$-{\rm div}a(x, u, \nabla u) + g(x, u, \nabla u) = f-{\rm div}F$$ where $a(.)$ is a Carathéodory function satisfying the classical condition of type Leray-Lions hypothesis, while $g(x, s, \xi)$ is a non-linear term which has a growth condition with respect to $\xi$ and no growth with respect to $s$, but it satisfies a sign condition on $s$

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 W1,pIn 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 ()