Stabilities in linear integrodifferential equations. (English) Zbl 0848.45003
Masuda, Kyûa (ed.) et al., Finite and infinite dimensional dynamics. Proceedings of the Japan-US joint conference, Kyoto, Japan, July 17-21, 1988. Kyoto: Kinokuniya. Lect. Notes Numer. Appl. Anal. 15, 31-46 (1996).
We consider a linear integrodifferential equation
\[
\dot x(t)= A(t) x(t)+ \int^t_0 B(t, s) x(s) ds, \tag{E}\(_0\)
\]
where \(A(t)\) and \(B(t, s)\) are \(n\times n\) matrix-valued continuous functions. The main purpose of this article is to give some characterizations for the uniform asymptotic stability of the zero solution of \((\text{E}_0)\).
For the entire collection see [Zbl 0840.00027].
For the entire collection see [Zbl 0840.00027].
MSC:
| 45M10 | Stability theory for integral equations |
| 45M05 | Asymptotics of solutions to integral equations |
| 45J05 | Integro-ordinary differential equations |
| 45F05 | Systems of nonsingular linear integral equations |
