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Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces

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  • Anna Kisiolek
  • Ireneusz Kubiaczyk

Abstract

We consider the second-order nonlinear difference equations of the form Δ ( r n − 1 Δ x n − 1 ) + p n f ( x n − k ) = h n . We show that there exists a solution ( x n ) , which possesses the asymptotic behaviour ‖ x n − a ∑ j = 0 n − 1 ( 1 / r j ) + b ‖ = o ( 1 ) , a , b ∈ ℝ . In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988). We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.

Suggested Citation

  • Anna Kisiolek & Ireneusz Kubiaczyk, 2005. "Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:983278
    DOI: 10.1155/IJMMS.2005.2769
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