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

• Main Authors: Muminov, M. I., Murid, A. H. M.
• Format: Article
• Language: English
• Published: De Gruyter 2020
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/87777/1/Mukhiddin%C3%89Muminov2020_ExistenceConditionsforPeriodicSolutions.pdf; http://eprints.utm.my/id/eprint/87777/; http://www.dx.doi.org/10.1515/math-2020-0010
• Institution: Universiti Teknologi Malaysia

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.