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.

中文翻译：

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具有分段常数参数的二阶中性延迟微分方程周期解的存在条件

摘要 在本文中，我们描述了一种求解具有 x″(t) + px″(t − 1) = qx([ t]) + f(t)，其中 [⋅] 表示最大整数函数，p 和 q 是非零实数或复数常数，f(t) 是复值周期函数。该方法将问题简化为代数方程组。我们给出了方程解的显式公式。我们还给出了一些先前关于解决方案唯一性的发现的反例。