Existence conditions for periodic solutions of second-order neutral delay differential equations with piecewise constant arguments

Abstract In this paper, we describe a method to solve the problem of finding periodic solutions for second-order neutral delay-differential equations with piecewise constant arguments of the form x ″( t ) + px ″( t − 1) = qx ([ t ]) + f ( t ), where [⋅] denotes the greatest integer function, p and q are nonzero real or complex constants, and f ( t ) is complex valued periodic function. The method reduces the problem to a system of algebraic equations. We give explicit formula for the solutions of the equation. We also give counter examples to some previous findings concerning uniqueness of solution.

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