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UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS

구윤회|Sang Il Choi
한국수학교육학회|2016.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제23권 제1호|pp. 1-12

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참고문헌

키워드

uniformly Lipschitz stabilityuniformly Lipschitz stability in variationexponentially asymptotic stabilityexponentially asymptotic stability in variation.
주제분류수학

초록

This paper shows that the solutions to the perturbed differential system y'=f(t,y)+\int_{t_0}^tg(s,y(s),Ty(s))ds+h(t,y(t)) have asymptotic property and uniform Lipschitz stability. To show these properties, we impose conditions on the perturbed part \int_{t_0}^tg(s,y(s),Ty(s))ds, h(t,y(t)), and on the fundamental matrix of the unperturbed system y'=f(t,y).

Abstract

This paper shows that the solutions to the perturbed differential system y'=f(t,y)+\int_{t_0}^tg(s,y(s),Ty(s))ds+h(t,y(t)) have asymptotic property and uniform Lipschitz stability. To show these properties, we impose conditions on the perturbed part \int_{t_0}^tg(s,y(s),Ty(s))ds, h(t,y(t)), and on the fundamental matrix of the unperturbed system y'=f(t,y).

참고문헌 (16)

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