On the Method of Lyapunov Functionals for a Linear First-Order Volterra Integrodifferential Equation with Delay on the Semiaxis

Sufficient conditions are established to ensure the estimation, boundedness, power-law absolute integrability on the semiaxis, the tendency to zero under the tendency to infinity of the independent variable of all solutions of the linear Volterra integrodifferential equation of the first order with delay. For this purpose, a generalized Lyapunov functional is constructed. An illustrative example is presented.