Solutions for a quasilinear elliptic equation with critical Sobolev exponent and perturbations on \({\mathbb{R}}^N\) (Q5933777)
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scientific article; zbMATH DE number 1604525
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solutions for a quasilinear elliptic equation with critical Sobolev exponent and perturbations on \({\mathbb{R}}^N\) |
scientific article; zbMATH DE number 1604525 |
Statements
Solutions for a quasilinear elliptic equation with critical Sobolev exponent and perturbations on \({\mathbb{R}}^N\) (English)
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14 June 2001
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quasilinear elliptic equations
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Sobolev critical exponent
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The author considers the quasilinear elliptic problem NEWLINE\[NEWLINE\begin{cases} NEWLINE- \operatorname{div}(|\nabla u|^{p-2} \nabla u) + c |u|^{p^*-2} u = |u|^{p^*-2} u + f(x,u) + h(x) \\ NEWLINEu \in W^{1,p}(\mathbb{R}^N), 2\leq p <N \end{cases} NEWLINE\]NEWLINE and study how the perturbations \(f\) and \(h\) affect the multiplicity of the solutions of the problem.
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