Compact embeddings and indefinite semilinear elliptic problems

Our purpose is to find positive solutions $u\in D^{1,2}({\text{rz}}^N)$ of the semilinear elliptic problem $-\text{laplace}u=h(x)u^{p-1}$ for $2<p$. The function $h$ may have an indefinite sign. Key ingredients are a $h$-dependent concentration-compactness Lemma and a characterization of compact embeddings of $D^{1,2}({\text{rz}}^N)$ into weighted Lebesgue spaces.