Periodicity and stability in neutral equations by Krasnoselskii’s fixed point theorem

In this paper, we consider a nonlinear neutral functional differential equation which arises from a transmission line model. By means of Krasnoselskii’s fixed point theorem, we obtain sufficient conditions of the existence of asymptotic periodic solutions. This paper is motivated by the difficulty encountered in the study of integrated electronic circuits which are composed of lossy transmission lines and nonlinear resistive loads with exponential VV–II characteristics. We also correct one of the results in [V.G. Angelov, Lossy transmission lines terminated by RR-loads with exponential VV–II characteristics, Nonlinear Anal. RWA 8 (2007) 579–589]. As an application, we show there is a periodic oscillation along the line when the load is a p–n diode.