Improved Stability and Instability Results for Neutral Integro-Differential Equations Including Infinite Delay

Abstract

In this article, we consider nonlinear neutral Volterra integro-differential equations (NVIDEs) including infinite delay. We prove three new theorems with regard to the stability, the uniform stability, and the instability of zero solution of the NVIDEs. The new results of this article include sufficient conditions and the technique of the proofs is based on the Lyapunov-Krasovskii functional (LKF) approach. By this article, some results that can be found in the literature are extended and improved from the linear case to nonlinear cases and contributed.