Asymptotic behavior of solutions to a linear Volterra integrodifferential system
Summary: We investigate the asymptotic behavior of solutions to a linear Volterra integro-differential system \(x'_i(t)=a_i(t)+b_i(t)x_i(t)+\sum^n_{j=1}\int^t_0 K_{ij}(t,s)x_j(s)ds\), \(t\in\mathbb R^+\), \(i=1,2,\dots,n\). 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.
linear Volterra integro-differential system
scientific article; zbMATH DE number 6306557
scientific article