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ISSN : 1226-0657

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Vol.23 No.2

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Boundedness in the nonlinear perturbed differential systems via t∞–similarity

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2016, v.23 no.2, pp.105-117
https://doi.org/10.7468/jksmeb.2016.23.2.105
GOO, YOON HOE
GOO,, Y. H. (2016). Boundedness in the nonlinear perturbed differential systems via t∞–similarity. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 23(2), 105-117, https://doi.org/10.7468/jksmeb.2016.23.2.105

Abstract

This paper shows that the solutions to the nonlinear perturbed differential system <TEX>$y{\prime}=f(t,y)+\int_{t_0}^{t}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$</TEX>, have the bounded property by imposing conditions on the perturbed part <TEX>$\int_{t_0}^{t}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$</TEX>, and on the fundamental matrix of the unperturbed system y&#x2032; = f(t, y) using the notion of h-stability.

keywords
h-stability, t<sub>∞</sub>-similarity, bounded, nonlinear nonautonomous system

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