Asymptotic behaviour of solutions of difference equations in Banach spaces
Anna Kisiołek
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 28 (2008), p. 5-13 / Harvested from The Polish Digital Mathematics Library
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In this paper we consider the first order difference equation in a Banach space Δxn=∑i=0∞anif(xn+i). We show that this equation has a solution asymptotically equal to a. As an application of our result we study the difference equation Δxn=∑i=0∞anig(xn+i)+∑i=0∞bnih(xn+i)+yn and give conditions when this equation has solutions. In this note we extend the results from [8,9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:271171 
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     volume = {28},
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Anna Kisiołek. Asymptotic behaviour of solutions of difference equations in Banach spaces. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 28 (2008) pp. 5-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1093/

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