On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments
Abstract 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 ) + p x ″ ( t − 1 ) = q x ( 2 [ t + 1 2 ] ) + f ( t ) $x''(t)+px''(t-1)=qx(2[\frac{t+1}{2}])+f(t)$...
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Format: | Article |
Language: | English |
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SpringerOpen
2017-10-01
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Series: | Advances in Difference Equations |
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Online Access: | http://link.springer.com/article/10.1186/s13662-017-1396-7 |
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author | Mukhiddin I Muminov |
author_facet | Mukhiddin I Muminov |
author_sort | Mukhiddin I Muminov |
collection | DOAJ |
description | Abstract 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 ) + p x ″ ( t − 1 ) = q x ( 2 [ t + 1 2 ] ) + f ( t ) $x''(t)+px''(t-1)=qx(2[\frac{t+1}{2}])+f(t)$ , where [ ⋅ ] $[\cdot]$ 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 $n+1$ 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. |
first_indexed | 2024-12-11T07:47:45Z |
format | Article |
id | doaj.art-ff96170e45f940269ddb68fd3c020dab |
institution | Directory Open Access Journal |
issn | 1687-1847 |
language | English |
last_indexed | 2024-12-11T07:47:45Z |
publishDate | 2017-10-01 |
publisher | SpringerOpen |
record_format | Article |
series | Advances in Difference Equations |
spelling | doaj.art-ff96170e45f940269ddb68fd3c020dab2022-12-22T01:15:25ZengSpringerOpenAdvances in Difference Equations1687-18472017-10-012017111710.1186/s13662-017-1396-7On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant argumentsMukhiddin I Muminov0Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi MalaysiaAbstract 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 ) + p x ″ ( t − 1 ) = q x ( 2 [ t + 1 2 ] ) + f ( t ) $x''(t)+px''(t-1)=qx(2[\frac{t+1}{2}])+f(t)$ , where [ ⋅ ] $[\cdot]$ 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 $n+1$ 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.http://link.springer.com/article/10.1186/s13662-017-1396-7differential equationpiecewise constant argumentperiodic solution |
spellingShingle | Mukhiddin I Muminov On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments Advances in Difference Equations differential equation piecewise constant argument periodic solution |
title | On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments |
title_full | On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments |
title_fullStr | On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments |
title_full_unstemmed | On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments |
title_short | On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments |
title_sort | on the method of finding periodic solutions of second order neutral differential equations with piecewise constant arguments |
topic | differential equation piecewise constant argument periodic solution |
url | http://link.springer.com/article/10.1186/s13662-017-1396-7 |
work_keys_str_mv | AT mukhiddinimuminov onthemethodoffindingperiodicsolutionsofsecondorderneutraldifferentialequationswithpiecewiseconstantarguments |