On quasilinear elliptic equations in \(\mathbb{R}^N\) (Q1809754)
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scientific article; zbMATH DE number 1370646
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On quasilinear elliptic equations in \(\mathbb{R}^N\) |
scientific article; zbMATH DE number 1370646 |
Statements
On quasilinear elliptic equations in \(\mathbb{R}^N\) (English)
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25 November 1999
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Summary: We give a result for the \(p\)-Laplacian operator complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation \(-\Delta u= h(x)u^q\) in \(\mathbb{R}^N\), where \(0< q<1\), to have a bounded positive solution. While Brézis and Kamin use the method of sub- and super solutions, we employ variational arguments for the existence of solutions.
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mountain-pass theorem
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\(p\)-Laplacian
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variational method
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