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

This paper provides a method of finding periodical solutions of the second-order neutral delay differential equations with piecewise constant arguments of the form $x''(t)+px''(t-1)=qx(2[\frac{t+1}{2}])+f(t)$ , where $[\cdot]$ 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.

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