Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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BOUNDEDNESS FOR NONLINEAR PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY

  • Im, Dong Man (Department of Mathematics Education Cheongju University)
  • Received : 2016.07.14
  • Accepted : 2016.10.13
  • Published : 2016.11.15
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Abstract

This paper shows that the solutions to the nonlinear perturbed differential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$, have bounded properties. To show these properties, we impose 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) using the notion of h-stability.

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References

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