Quasilinear elliptic systems with critical Sobolev exponents in \(\mathbb {R}^N\) (Q875259)
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scientific article; zbMATH DE number 5142208
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quasilinear elliptic systems with critical Sobolev exponents in \(\mathbb {R}^N\) |
scientific article; zbMATH DE number 5142208 |
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Quasilinear elliptic systems with critical Sobolev exponents in \(\mathbb {R}^N\) (English)
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13 April 2007
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The paper deals with a quasilinear system involving the \(p\)-Laplacian on \(\mathbb R^N\), the critical Sobolev exponent and a parameter \(\lambda>0\). The existence of a nontrivial weak solution provided \(\lambda\) is sufficiently small is shown. The main technical tools are the verification of the Palais-Smale condition at levels in a specific range and application of the mountain pass theorem.
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\(p\)-Laplacian
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weak solution
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Palais-Smale condition
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mountain pass theorem
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concentration-compactness principle
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