Asymptotic behavior of Volterra integrodifferential equations (Q1363018)

The asymptotic behavior and boundedness of the solution of the Volterra integrodifferential equation \[ x'(t)= A(t)x(t)+ \int_0^t C(t,s)x(s)ds+ \int_0^t G(t,s,x(s))ds+ f(t), \] where \(x\in\mathbb{R}^n\), \(A(t)\) and \(C(t,s)\) are continuous \(n\times n\) matrices, and \(f(t)\) is continuous \(n\)-vectors, is studied. The function \(G(t,s,x(s))\) is the unknown parameter perturbation with respect to the state \(x(s)\) in the linear integral term. Different theorems and corollaries are proved.