A Volterra inequality with the power type nonlinear kernel.
We improve (in some sense) a recent theorem due to Banas and Knap (1989) about the existence of integrable solutions of a functional-integral equation.
A Cauchy problem for an abstract nonlinear Volterra integrodifferential equation is considered. Existence and uniqueness results are shown for any given time interval under weak time regularity assumptions on the kernel. Some applications to the heat flow with memory are presented.