Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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BOUNDEDNESS IN NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY

  • Im, Dong Man (Department of Mathematics Education Cheongju University) ;
  • Goo, Yoon Hoe (Department of Mathematics Hanseo University)
  • Received : 2016.09.09
  • Accepted : 2016.12.20
  • Published : 2016.12.30
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Abstract

This paper shows that the solutions to nonlinear perturbed differential system $$y^{\prime}= f(t,y)+{\int_{t_{0}}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_{0}}^{t}g(s,y(s))ds,\;h(t, y(t),\;Ty(t))$, 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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