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

• Main Author: Muminov, M. I.
• Format: Article
• Language: English
• Published: Springer International Publishing 2017
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/74839/1/MukhiddinIMuminov2017_OntheMethodofFindingPeriodicSolutions.pdf; http://eprints.utm.my/id/eprint/74839/; https://www.scopus.com/inward/record.uri?eid=2-s2.0-85032030944&doi=10.1186%2fs13662-017-1396-7&partnerID=40&md5=db91bca7b1436a96f8006e19a28c4f77
• Institution: Universiti Teknologi Malaysia

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[t+12])+f(t), where [ ⋅ ] 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.