Existence of solutions for quasilinear degenerate elliptic equations

• Main Authors: Y. Akdim, E. Azroul, A. Benkirane
• Format: Article
• Language: English
• Published: Texas State University 2001-11-01
• Series: Electronic Journal of Differential Equations
• Subjects: Weighted Sobolev spaces; Hardy inequality; Quasilinear degenerate elliptic operators.
• Online Access: http://ejde.math.txstate.edu/Volumes/2001/71/abstr.html

In this paper, we study the existence of solutions for quasilinear degenerate elliptic equations of the form $A(u)+g(x,u,abla u)=h$, where $A$ is a Leray-Lions operator from $W_0^{1,p}(Omega,w)$ to its dual. On the nonlinear term $g(x,s,xi)$, we assume growth conditions on $xi$, not on $s$, and a sign condition on $s$.