Neutral Operator and Neutral Differential Equation

الملخص EN

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.