Asymptotic solutions of semilinear elliptic equations (Q791756)
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scientific article; zbMATH DE number 3851590
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic solutions of semilinear elliptic equations |
scientific article; zbMATH DE number 3851590 |
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Asymptotic solutions of semilinear elliptic equations (English)
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1984
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Semilinear elliptic equations of the form \(Lu\equiv \Delta u-p(| x|)u+uf(x,u)=0\) are considered in exterior domains in \({\mathbb{R}}^ n\) for \(n\geq 2\). Both necessary and sufficient conditions are established for such equations to have positive solutions with prescribed asymptotic behavior as \(| x| \to \infty\).
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asymptotic solutions
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semilinear elliptic equations
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supersolution
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subsolution
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exterior domain
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positive solutions
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