  In this paper we prove existence of radial solutions for the nonlinear
elliptic problem
  \[ -\mathrm{div}(A(|x|)\nabla u)+V(|x|)u=K(|x|)f(u) \quad \text{in
}\mathbb{R}^{N}, \]
  \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.
