Compact embeddings and indefinite semilinear elliptic problems

Details Compact embeddings and indefinite semilinear elliptic problems Compact embeddings and indefinite semilinear elliptic problems

2002-06-07

arxiv.org/abs/math/0206069v1

Mathematics

Analysis of PDEs

Scientific paper

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

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