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Boundedness in nonlinear perturbed differential systems via $t_{\infty}$-similarity

구윤회|임동만
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2016.12|한국수학논문집 (Korean Journal of Mathematics)|제24권 제4호|pp. 723-736|DOI https://doi.org/10.11568/kjm.2016.24.4.723

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키워드

bounded$h$-stabilitynonlinear nonautonomous system.$t_{infty}$-similarity
주제분류수학

초록

This paper shows that the solutions to nonlinear perturbed differential system $$ y'=f(t,y)+\int_{t_0}^tg(s,y(s))ds+h(t,y(t),Ty(t)) $$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part $\int_{t_0}^tg(s,y(s))ds$, $h(t,y(t),Ty(t))$, and on the fundamental matrix of the unperturbed system $y'=f(t,y)$ using the notion of $h$-stability.

Abstract

This paper shows that the solutions to nonlinear perturbed differential system $$ y'=f(t,y)+\int_{t_0}^tg(s,y(s))ds+h(t,y(t),Ty(t)) $$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part $\int_{t_0}^tg(s,y(s))ds$, $h(t,y(t),Ty(t))$, and on the fundamental matrix of the unperturbed system $y'=f(t,y)$ using the notion of $h$-stability.

참고문헌 (16)

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