Stability implications on the asymptotic behavior of nonlinear systems

[摘要] In this paper we generalize Bownds' Theorems (1) to the systemsdY(t)dt=A(t)Y(t)anddX(t)dt=A(t)X(t)+F(t,X(t)). Moreover we also show that there always exists a solutionX(t)ofdXdt=A(t)X+B(t)for whichlimt→∞sup‖X(t)‖>o(=∞)if there exists a solutionY(t)for whichlimt→∞sup‖Y(t)‖>o(=∞).

[学科分类] 数学（综合）