Abstract
In this paper we consider a neutral differential equation with variable delays and give some new conditions for the boundedness and stability results by using of Krasnoselskii’s fixed point theorem. Namely, a necessary and sufficient condition ensuring the asymptotic stability is proved, which improves and generalizes some results due to Burton and Furumochi (Dyn Syst Appl 11:499–519, 2002), and Jin and Luo (Nonlinear Anal 68:3307–3315, 2008). Finally, an example is exhibited to illustrate the effectiveness of the proposed results.
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