On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments
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 f...
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| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2017
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| 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 |
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| Institution: | Universiti Teknologi Malaysia |
| Language: | English |
| Summary: | 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. |
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