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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.23 No.1

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UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS

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.1, pp.1-12
https://doi.org/10.7468/jksmeb.2016.23.1.1
CHOI, SANG IL
GOO, YOON HOE
CHOI,, S. I. , & GOO,, Y. H. (2016). UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 23(1), 1-12, https://doi.org/10.7468/jksmeb.2016.23.1.1

Abstract

This paper shows that the solutions to the perturbed differential system <TEX>$y^{\prime}=f(t, y)+\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))$</TEX> have asymptotic property and uniform Lipschitz stability. To show these properties, we impose conditions on the perturbed part <TEX>$\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))$</TEX>, and on the fundamental matrix of the unperturbed system y' = f(t, y).

keywords
uniformly Lipschitz stability, uniformly Lipschitz stability in variation, exponentially asymptotic stability, exponentially asymptotic stability in variation

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