International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 1, Pages 105-112
doi:10.1155/S0161171282000106
Stability implications on the asymptotic behavior of nonlinear systems
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.
Abstract
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 limt→∞sup‖X(t)‖>o(=∞) if there exists a solution Y(t) for which limt→∞sup‖Y(t)‖>o(=∞).