Stability in nonlinear Levin-Nohel integro-differential equations

Abstract

In this paper, we use a Banach fixed point theorem to obtain stability
results of the zero solution of a nonlinear Levin-Nohel integro-differential
equations with functional delay. To be more precise, we are concerned with the following equation
\begin{equation*}
x^{\prime }\left( t\right) =-\int_{t-\tau \left( t\right) }^{t}a\left(
t,s\right) g\left( x\left( s\right) \right) ds.
\end{equation*}
The obtained theorems improve previous results due to Burton \cite{bur1}, Becker and Burton \cite{bec} and Jin and Luo \cite{jin} and Dung \cite{dun}. The last equation with several delay terms is studied.