Compact embeddings and indefinite semilinear elliptic problems

Matthias Schneider

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arXiv · math/0206069

Compact embeddings and indefinite semilinear elliptic problems

Matthias Schneider

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Abstract

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 $2<p$. The function $h$ may have an indefinite sign. Key ingredients are a $h$-dependent concentration-compactness Lemma and a characterization of compact embeddings of $D^{1,2}(\rz^N)$ into weighted Lebesgue spaces.

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Matthias Schneider. 2002-06-07. Compact embeddings and indefinite semilinear elliptic problems. https://arxiv.org/abs/math/0206069

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