Entropy solution for a nonlinear degenerate elliptic problem with Dirichlet-type boundary condition and singular term
Hassan El Hamri, Morad Ouboufettal, Akdim Youssef · Gulf Journal of Mathematics · 2025
This paper establishes the existence of entropy solutions for a class of nonlinear elliptic equations governed by a degenerate coercive operator and featuring a singular right-hand side, exemplified by the model case: -div( (|∇u - Θ(u)|p-2 (∇u - Θ(u)) ) / ( (1+|u|)λ(p-1) ) ) + |u|q-1u = f / uγ in Ω,u ≥ 0 in Ω,u = 0 on ∂Ω, with Ω is a bounded open domain in RN (N≥2), p>1, λ≥0, γ≥0, q≥1, f is a non-negative function that belongs to L1(Ω) and Θ is assumed to be continuous on the real line R.