Sobolev type embeddings and an inhomogeneous quasilinear elliptic equation on RNRN with singular weights

In this paper we build a Sobolev type embedding from a weighted Sobolev space into a weighted L1L1 space on the entire space RNRN. As applications, we study the existence and the uniqueness of radial solutions of the inhomogeneous quasilinear elliptic equation {−div(|∇u|p−2∇u)+V(|x|)|u|q−2u=Q(|x|),x∈RN,u(x)→0,|x|→∞ with singular radial weighted functions VV and QQ.