Neutral operator and neutral differential equation

Abstract

In this paper, we discuss the properties of the neutral operator (Ax)(t)=x(t)-cx(t-δ(t)), and by applying coincidence degree theory and fixed point index theory, we obtain sufficient conditions for the existence, multiplicity, and nonexistence of (positive) periodic solutions to two kinds of second-order differential equations with the prescribed neutral operator. © 2011 Jingli Ren et al.