• Title, Summary, Keyword: asymptotic stability

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LIPSCHITZ AND ASYMPTOTIC STABILITY OF PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS

  • Choi, Sang Il;Goo, Yoon Hoe
    • The Pure and Applied Mathematics
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    • v.22 no.1
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    • pp.1-11
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    • 2015
  • The present paper is concerned with the notions of Lipschitz and asymptotic for perturbed functional differential system knowing the corresponding stability of functional differential system. We investigate Lipschitz and asymptotic stability for perturbed functional differential systems. The main tool used is integral inequalities of the Bihari-type, and all that sort of things.

On asymptotic Stability in nonlinear differential system

  • An, Jeong-Hyang
    • Journal of the Korea Industrial Information Systems Research
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    • v.11 no.5
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    • pp.62-66
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    • 2006
  • We investigate various $\Phi(t)-stability$ of comparison differential equations and we abtain necessary and/or sufficient conditions for the uniform asymptotic and exponential asymptotic stability of the nonlinear differential equation x'=f(t, x).

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LIPSCHITZ AND ASYMPTOTIC STABILITY FOR PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS

  • Goo, Yoon Hoe
    • The Pure and Applied Mathematics
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    • v.21 no.1
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    • pp.11-21
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    • 2014
  • The present paper is concerned with the notions of Lipschitz and asymptotic stability for perturbed nonlinear differential system knowing the corresponding stability of nonlinear differential system. We investigate Lipschitz and asymtotic stability for perturbed nonlinear differential systems. The main tool used is integral inequalities of the Bihari-type, in special some consequences of an extension of Bihari's result to Pinto and Pachpatte, and all that sort of things.

ASYMPTOTIC STABILITY OF COMPETING SPECIES

  • Kim, June Gi
    • Korean Journal of Mathematics
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    • v.4 no.1
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    • pp.39-43
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    • 1996
  • Large-time asymptotic behavior of the solutions of interacting population reaction-diffusion systems are considered. Polynomial stability was proved.

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UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS

  • CHOI, SANG IL;GOO, YOON HOE
    • The Pure and Applied Mathematics
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    • v.23 no.1
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    • pp.1-12
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    • 2016
  • 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).

UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY OF PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS

  • Im, Dong Man;Goo, Yoon Hoe
    • Korean Journal of Mathematics
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    • v.24 no.1
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    • pp.1-13
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    • 2016
  • This paper shows that the solutions to the perturbed functional dierential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic property. To sRhow these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y^{\prime}=f(t,y)$.

UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC BEHAVIOR OF PERTURBED DIFFERENTIAL SYSTEMS

  • Choi, Sang Il;Goo, Yoon Hoe
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.3
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    • pp.429-442
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    • 2016
  • In this paper we show that the solutions to the perturbed differential system $$y^{\prime}=f(t,y)+{\int}_{to}^{t}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic behavior by imposing conditions on the perturbed part $\int_{to}^{t}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system y' = f(t, y).