A note on the qualitative behaviors of non-linear Volterra integro-differential equation

AbstractThis paper considers a scalar non-linear Volterra integro-differential equation. We establish sufficient conditions which guarantee that the solutions of the equation are stable, globally asymptotically stable, uniformly continuous on [0, ∞), and belongs to L1[0, ∞) and L2[0, ∞) and have bounded derivatives. We use the Lyapunov’s direct method to prove the main results. Examples are also given to illustrate the importance of our results. The results of this paper are new and complement previously known results