A projected discrete Gronwall's inequality with sub-exponential growth |
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Authors: | Linfeng Zhou |
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Institution: | Department of Mathematics , Sichuan University , Chengdu, Sichuan , P.R. China |
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Abstract: | Along with the increasing interest in (h, k)-dichotomy, more attentions are paid to sub-exponential growth in research of asymptotic behaviours. In this paper, we generalize a projected discrete Gronwall's inequality given in J. Differ. Equ. Appl. 10 (2004), 661–689] to a general one, which may include both terms of sub-exponential growth inside the summation and non-monotonic terms outside the summation. We demonstrate our results with concrete non-monotonic functions and sub-exponential functions. We apply our results to estimating bounded solutions of a non-linear difference equation with an (h, k)-dichotomy. |
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Keywords: | Gronwall's inequality difference equation sub-exponential growth non-monotonicity (h k)-dichotomy |
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