Existence of Solutions for Quasilinear Degenerate Elliptic Equations

Abstract

In this paper, we study the existence of solutions for quasilinear degenerate elliptic equations of the form A(u) + g(x, u, ∇u) = h where A is a Leray-Lions operator from W^1,p₀ (Ω, w) to its dual. On the nonlinear term g(x, s, ξ), we assume growth conditions on ξ, not on s, and a sign condition on s.