UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS

CHOI, SANG IL;GOO, YOON HOE

• Accepted : 2016.01.27
• Published : 2016.02.28
• 27 15

Abstract

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

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