International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 1, Pages 105-112

Stability implications on the asymptotic behavior of nonlinear systems

Kuo-Liang Chiou

Department of Mathematics, Wayne State University, Detroit 48202, Michigan, USA

Received 20 July 1978

Copyright © 1982 Kuo-Liang Chiou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we generalize Bownds' Theorems (1) to the systems dY(t)dt=A(t)Y(t) and dX(t)dt=A(t)X(t)+F(t,X(t)). Moreover we also show that there always exists a solution X(t) of dXdt=A(t)X+B(t) for which limtsupX(t)>o(=) if there exists a solution Y(t) for which limtsupY(t)>o(=).