l-solutions and stability analysis of difference equations using the Kummer’s test |
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Authors: | I Gy?ri L Horváth |
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Institution: | Department of Mathematics, University of Pannonia, Egyetem u. 10, 8200 Veszprém, Hungary |
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Abstract: | We address the p-summability and asymptotic stability properties in nonautonomous linear difference equations. We focus our discussion on two kind of difference equations. The first one is a first order system of linear nonautonomous difference equations, and our discussion involves the use of Kummer’s convergence test. The second one is a linear nonautonomous scalar higher order difference equation. In this case our discussion is based on a recently introduced transformation of a higher order system into a first-step recursion, where the companion matrices are well treatable from our point of view. We give insight on our ideas that are behind our methods, prove new results, and show applications. |
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Keywords: | Difference equations lp Solutions Stability Companion matrix |
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