Existence and multiplicity results for some quasilinear elliptic equation with weights

Using variational methods, we show the existence and multiplicity of solutions of singular boundary value problems of the type −div(|x|−αA(|∇u|)∇u) = |x|−βf (x,u) in Ω, u =0 on ∂Ω, where the numbers α and β, as well as the functions A and f satisfy certain conditions. © 2007 Elsevier Inc. All rights reserved.