On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space (Q2901936)
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scientific article; zbMATH DE number 6062433
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space |
scientific article; zbMATH DE number 6062433 |
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31 July 2012
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polyharmonic elliptic system
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Green function
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Kato class
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Shauder fixed point theorems
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On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space (English)
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The author proves two existence results concerning positive continuous solutions of a nonlinear polyharmonic system in the half space \(\mathbb R^n_+\). The nonlinear term is required to satisfy some conditions related to the Kato class. The tools used by the author are based on potential theory, in particular on estimates for the Green function, Shauder fixed point arguments and properties of the functions belonging to the Kato class. Let us point out that the paper is enriched by an application of the main result.
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