On the existence of positive solutions for a nonlocal elliptic problem involving the \(p\)-Laplacian and the generalized Lebesgue space \(L^{p(x)}(\Omega )\). (Q621535)
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scientific article; zbMATH DE number 5844182
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of positive solutions for a nonlocal elliptic problem involving the \(p\)-Laplacian and the generalized Lebesgue space \(L^{p(x)}(\Omega )\). |
scientific article; zbMATH DE number 5844182 |
Statements
On the existence of positive solutions for a nonlocal elliptic problem involving the \(p\)-Laplacian and the generalized Lebesgue space \(L^{p(x)}(\Omega )\). (English)
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2 February 2011
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The questions of existence of positive solutions for nonlocal problems are investigated. The Dirichlet problem for the equation \(-\Delta _{p} u=| u| _{q(x)}^{\alpha (x)}\) is considered. Under certain relations among \(\alpha \),\(q\), \(p\) and the space dimension existence of a positive solution is proved. The \((p_1,p_2)\)-Laplacian system is also considered.
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\(p\)-Laplacian
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space dependent power
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space dependent norm
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positive solution
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