On the decomposition problem of stability for Volterra integro- differential equations (Q1178384)

Consider the system \(\dot x_ i=A_{ii}(t)x_ i+\sum^ r_{\scriptstyle j=1\atop j\neq i}A_{ij}x_ j+\int^ t_ 0\left[C_{ii}(t,s)x_ i(s)+\sum^ r_{\scriptstyle j=1\atop j\neq i}C_{ij}(t,s)x_ j(s)\right]ds+f_ i(t)\), \(i=1,2,\dots,r\), where \(x_ i\in R^{n_ i}\), \(A_{ij}(t)\) and \(C_{ij}(t,s)\) are \(n_ i\times n_ j\) matrices of continuous functions. The authors discuss the stability of this system either for the homogeneous or nonhomogeneous cases. The boundedness of the solutions is also studied.