UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS

• Journal title : The Pure and Applied Mathematics
• Volume 23, Issue 1,  2016, pp.1-12
• Publisher : Korea Society of Mathematical Education
• DOI : 10.7468/jksmeb.2016.23.1.1
Title & Authors
UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS
CHOI, SANG IL; GOO, YOON HOE;

Abstract
This paper shows that the solutions to the perturbed differential system $\small{y^{\prime}=f(t, y)+\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))}$ have asymptotic property and uniform Lipschitz stability. To show these properties, we impose conditions on the perturbed part $\small{\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))}$, 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;
Language
English
Cited by
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