Positive solution of second-order multi-point boundary value problems for finite difference equation with a \(p\)-Laplacian (Q949248)
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scientific article; zbMATH DE number 5354592
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive solution of second-order multi-point boundary value problems for finite difference equation with a \(p\)-Laplacian |
scientific article; zbMATH DE number 5354592 |
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Positive solution of second-order multi-point boundary value problems for finite difference equation with a \(p\)-Laplacian (English)
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21 October 2008
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The paper is concerned with the boundary value problems for the following second-order difference equation with \(p\)-Laplacian: \[ \Delta(\varphi_p(\Delta u(k)))+\lambda q(k)f(k,u(k))=0, \] subject to multi-point boundary value conditions. The approach is to use a fixed point theorem on the cone due to Krasnosel'skii. At least one positive solution is shown to exist.
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boundary value problem
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\(p\)-Laplacian
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positive solution
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second-order difference equation
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multi-point boundary value conditions
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