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On the asymptotic behavior of solution of certain systems of Volterra equations. (English) Zbl 1424.39033

Summary: This paper is concerned with the asymptotic property of the solution of a system of the linear Volterra difference equations. The criterion for the existence of a solution of the considered system that is asymptotically equivalent to a given sequence is established. The results generalize some recent results. The results presented here improve and generalize the results published by J. Diblík and E. Schmeidel [Appl. Math. Comput. 218, No. 18, 9310–9320 (2012; Zbl 1250.39002); with M. Růžičková, Comput. Math. Appl. 59, No. 8, 2854–2867 (2010; Zbl 1202.39013)]. Unlike in those works, here periodicity of the nonhomogeneous term of the equation is not assumed. Examples illustrate the obtained results.

MSC:

39A22 Growth, boundedness, comparison of solutions to difference equations
39A10 Additive difference equations
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