| Summary: | 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 ) + p x ″ ( t − 1 ) = q x ( 2 [ t + 1 2 ] ) + f ( t ) $x''(t)+px''(t-1)=qx(2[\frac{t+1}{2}])+f(t)$ , 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 $n+1$ 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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