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Asymptotic bounds for linear difference systems. (English) Zbl 1191.39016
Summary: This paper describes asymptotic properties of solutions of some linear difference systems. First we consider system of a general form and estimate its solutions by use of a solution of an auxiliary scalar difference inequality assuming that this solution admits certain properties. Then applying this result to linear difference systems of a variable order with constant (or bounded) coefficients we derive effective asymptotic criteria for such systems. Beside it, we give applications of these results to numerical analysis of vector differential equations with infinite lags.
MSC:
39A22Growth, boundedness, comparison of solutions (difference equations)
39A06Linear equations (difference equations)
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