Existence of Solutions for Quasilinear Degenerate Elliptic Equations
Southwest Texas State University, Department of Mathematics
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 W1,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.
Weighted Sobolev spaces, Hardy inequality, Quasilinear degenerate elliptic operators
Akdim, Y., Azroul, E., & Benkirane, A. (2001). Existence of solutions for quasilinear degenerate elliptic equations. <i>Electronic Journal of Differential Equations, 2001</i>(71), pp. 1-19.