BOUNDEDNESS IN THE NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY

GOO, YOON HOE

• Accepted : 2016.05.13
• Published : 2016.05.31
• 31 18

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 the bounded 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) using the notion of h-stability.

Keywords

h-stability;t-similarity;bounded;nonlinear nonautonomous system

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