Perron-type stability theorems for neutral equations Original Research Article

In this paper, we present two Perron-type asymptotic stability results for a neutral functional differential equation of the form View the MathML source when the linear part (x′(t)=Sx(t)+Px(t−r)) is asymptotically stable. In particular, Q and G are allowed to be unbounded functions of t and Q need not be differentiable. The results are based on Krasnoselskiiʹs fixed point theorem. It is to be emphasized that, unlike Perron, we obtain only asymptotic stability because of the unboundedness of Q and G.