Existence of ground states with exponential decay for semi-linear elliptic equations in \({\mathbb{R}}^ n\) (Q1119822)
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scientific article; zbMATH DE number 4097891
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of ground states with exponential decay for semi-linear elliptic equations in \({\mathbb{R}}^ n\) |
scientific article; zbMATH DE number 4097891 |
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Existence of ground states with exponential decay for semi-linear elliptic equations in \({\mathbb{R}}^ n\) (English)
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1988
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The authors prove under suitable assumptions on f the existence of positive entire solutions of \(-\Delta u+f(x,u)=0\) on \({\mathbb{R}}^ n\) decaying exponentially to zero by studying the problem in certain exponentially weighted spaces. For a different technique and slightly different assumptions see \textit{E. Noussair} [Bull. Lond. Math. Soc. 19, 443-448 (1987; Zbl 0633.35025)].
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existence
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positive entire solutions
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decaying exponentially
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exponentially weighted spaces
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