Stability conditions for a mixed linear Levin–Nohel integrodifferential system

Abstract

We use the Banach fixed point theorem to obtain stability results of the zero solution for a mixed linear Levin–Nohel integrodifferential system. To be more precise, we are concerned with the system

$$x^{\prime }(t)+{\int }_{t-\tau (t)}^{t}C(t,s)x(s)ds+B(t)x(t-h(t))=0,$$

where the importance of studying this system is that it generalizes results due to Burton (2004), Becker and Burton (2006), Jin and Luo (2009) and Dung (2013), from one dimension to $n$ dimensions. The last system with several delays terms is discussed as well.