Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System

Abstract

We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system $x_i^{\prime }(t)=a_i(t)+b_i(t)x_i(t)+{\sum }_{j=1}^n\mathrm{‍}{\int }_0^t\mathrm{‍}{K}_{ij}(t,s)x_j(s)ds,t\in {ℝ}^{+}$, $i=\mathrm{1,2},\dots ,n.$ We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.