Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ASYMPTOTIC PROPERTY OF PERTURBED NONLINEAR SYSTEMS

  • Im, Dong Man (Department of Mathematics Education Cheongju University) ;
  • Choi, Sang Il (Department of Mathematics Hanseo University) ;
  • Goo, Yoon Hoe (Department of Mathematics Hanseo University)
  • Received : 2016.12.11
  • Accepted : 2017.01.09
  • Published : 2017.02.15
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Abstract

In this paper, we show that the solutions to perturbed differential system $$y^{\prime}=f(t,y)+{{\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$ have asymptotic property by imposing conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y).

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References

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