Radial nonlinear elliptic problems with singular or vanishing potentials

In this paper we prove existence of radial solutions for the nonlinear elliptic problem $$-\mathrm{d}\mathrm{i}\mathrm{v}(A(\mathrm{\mid }x\mathrm{\mid })\mathrm{\nabla }u)+V(\mathrm{\mid }x\mathrm{\mid })u=K(\mathrm{\mid }x\mathrm{\mid })f(u)\text{in }{\mathbb{R}}^N,$$ \noindent with suitable hypotheses on the radial potentials $A,V,K$. We first get compact embeddings of radial weighted Sobolev spaces into sum of weighted Lebesgue spaces, and then we apply standard variational techniques to get existence results.