Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY OF PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS

  • Im, Dong Man (Department of Mathematics Education Cheongju University) ;
  • Goo, Yoon Hoe (Department of Mathematics Hanseo University)
  • Received : 2015.09.04
  • Accepted : 2016.02.02
  • Published : 2016.03.30
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Abstract

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 $y^{\prime}=f(t,y)$.

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References

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Cited by

  1. UNIFORMLY LIPSCHITZ STABILITY OF PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS vol.30, pp.2, 2016, https://doi.org/10.14403/jcms.2017.30.2.273