On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments

Abstract

This paper provides a method of finding periodical solutions of the second-order neutral delay differential equations with piecewise constant arguments of the form x″(t)+px″(t−1)=qx(2[t+12])+f(t), where [ ⋅ ] denotes the greatest integer function, p and q are nonzero constants, and f is a periodic function of t. This reduces the 2n-periodic solvable problem to a system of n+ 1 linear equations. Furthermore, by applying the well-known properties of a linear system in the algebra, all existence conditions are described for 2n-periodical solutions that render explicit formula for these solutions.