Quasilinear Elliptic Equations With Neumann Boundary And Singularity

LetΩbe a bounded domain with a smooth C² boundary in R^N(N≥3), 0∈(?), and n denote the unit outward normal to (?)Ω. We are concerned with the Neumann boundary problems: -div(|x|^α|â–½u|^p-2â–½u) = |x|^βu^{p(α,β)-1}-λ|x|^γu^p-1, u{x) > 0,x∈Ω,(?)u/(?)n= 0 on (?)Ω, where 1 p,γ>α- p. For various parametersα,βorγ, we establish some existence results of the solutions in the case 0∈Ωor 0∈(?)Ω.