Weighted Asymptotically Periodic Solutions of Linear Volterra Difference Equations

Josef Diblík, Miroslava Růžičková, Ewa Schmeidel and Małgorzata Zbąszyniak

Abstract and Applied Analysis, 2011, vol. 2011, 1-14

Abstract:

A linear Volterra difference equation of the form ð ‘¥ ( ð ‘› + 1 ) = ð ‘Ž ( ð ‘› ) + ð ‘ ( ð ‘› ) ð ‘¥ ( ð ‘› ) + ∑ ð ‘› ð ‘– = 0 ð ¾ ( ð ‘› , ð ‘– ) ð ‘¥ ( ð ‘– ) , where ð ‘¥ ∶ â„• 0 → â„ , ð ‘Ž ∶ â„• 0 → â„ , ð ¾ âˆ¶ â„• 0 × â„• 0 → â„ and ð ‘ âˆ¶ â„• 0 → ℠⧵ { 0 } is 𠜔 -periodic, is considered. Sufficient conditions for the existence of weighted asymptotically periodic solutions of this equation are obtained. Unlike previous investigations, no restriction on ∠𠜔 − 1 ð ‘— = 0 ð ‘ ( ð ‘— ) is assumed. The results generalize some of the recent results.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:370982

DOI: 10.1155/2011/370982

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