Results for degenerate nonlinear elliptic equations involving a Hardy potential

Consider the problem(P){−div(A(x,u,∇u))=λus|x|p+f(x)in Ω,u(x)⩾0in Ω,u(x)=0on ∂Ω, where Ω   is an open bounded subset of RNRN (N⩾3N⩾3), 1• The threshold on s   to have existence or nonexistence of solution in some weak sense is s=(p−1)(1−θ)s=(p−1)(1−θ). Moreover a bound on λ   is needed to have solution in the critical case s=(p−1)(1−θ)s=(p−1)(1−θ).
• The regularity of the solution according to the summability of f.