European Journal of Applied Mathematics



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On matrix differential equations with several unbounded delays


J. CERMÁK a1
a1 Institute of Mathematics, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic email: cermak.j@fme.vutbr.cz

Article author query
cermak j   [Google Scholar] 
 

Abstract

The paper focuses on the matrix differential equation \[ \dot y(t)=A(t)y(t)+\sum_{j=1}^{m}B_j(t)y(\tau_j(t))+f(t),\quad t\in I=[t_0,\infty)\vspace*{-3pt} \] with continuous matrices $A$, $B_j$, a continuous vector $f$ and continuous delays $\tau_j$ satisfying $\tau_k\circ\tau_l =\tau_l\circ\tau_k$ on $I$ for any pair $\tau_k,\tau_l$. Assuming that the equation \[ \dot y(t)=A(t)y(t)\] is uniformly exponentially stable, we present some asymptotic bounds of solutions $y$ of the considered delay equation. A system of simultaneous Schröder equations is used to formulate these asymptotic bounds.

(Published Online July 25 2006)
(Received September 28 2005)
(Revised April 5 2006)