Multiple nonnegative solutions for BVPs of fourth-order difference equations
<p/> <p>First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ<sup>4</sup><it>x</it>(<it>t</it>-2) = <it>a</it>(<it>t</it>)<it...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2006-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2006/089585 |
| Summary: | <p/> <p>First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ<sup>4</sup><it>x</it>(<it>t</it>-2) = <it>a</it>(<it>t</it>)<it>f</it>(<it>x</it>(<it>t</it>)),<it>t</it> ∈ [2, <it>T</it>], <it>x</it>(0) = <it>x</it>(<it>T</it> + 2) = 0, Δ<sup>2</sup><it>x</it>(0) = Δ<sup>2</sup><it>x</it>(<it>T</it>) = 0 are established by using the well-known Leggett-Williams fixed point theorem, and then, for arbitrary positive integer <it>m</it>, existence results for at least 2<it>m</it>-1 nonnegative solutions are obtained.</p> |
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| ISSN: | 1687-1839 1687-1847 |