Periodic solutions for neutral nonlinear differential equations with functional delay
We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral differential equation with functional delay $$ x'(t) = -a(t)x(t)+ c(t)x'(t-g(t))+ q(t, x(t), x(t-g(t)) $$ has a periodic solution. Also, by transforming the problem to an integral equation we are able, using...
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| Format: | Article |
| Language: | English |
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Texas State University
2003-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/102/abstr.html |
| _version_ | 1818563869699735552 |
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| author | Youssef N. Raffoul |
| author_facet | Youssef N. Raffoul |
| author_sort | Youssef N. Raffoul |
| collection | DOAJ |
| description | We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral differential equation with functional delay $$ x'(t) = -a(t)x(t)+ c(t)x'(t-g(t))+ q(t, x(t), x(t-g(t)) $$ has a periodic solution. Also, by transforming the problem to an integral equation we are able, using the contraction mapping principle, to show that the periodic solution is unique. |
| first_indexed | 2024-12-14T01:21:58Z |
| format | Article |
| id | doaj.art-6888e2945c454207824b617aa81d85d2 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T01:21:58Z |
| publishDate | 2003-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-6888e2945c454207824b617aa81d85d22022-12-21T23:22:21ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-10-01200310217Periodic solutions for neutral nonlinear differential equations with functional delayYoussef N. RaffoulWe use Krasnoselskii's fixed point theorem to show that the nonlinear neutral differential equation with functional delay $$ x'(t) = -a(t)x(t)+ c(t)x'(t-g(t))+ q(t, x(t), x(t-g(t)) $$ has a periodic solution. Also, by transforming the problem to an integral equation we are able, using the contraction mapping principle, to show that the periodic solution is unique.http://ejde.math.txstate.edu/Volumes/2003/102/abstr.htmlKrasnoselskiineutralnonlinearintegral equationperiodic solutionunique solution. |
| spellingShingle | Youssef N. Raffoul Periodic solutions for neutral nonlinear differential equations with functional delay Electronic Journal of Differential Equations Krasnoselskii neutral nonlinear integral equation periodic solution unique solution. |
| title | Periodic solutions for neutral nonlinear differential equations with functional delay |
| title_full | Periodic solutions for neutral nonlinear differential equations with functional delay |
| title_fullStr | Periodic solutions for neutral nonlinear differential equations with functional delay |
| title_full_unstemmed | Periodic solutions for neutral nonlinear differential equations with functional delay |
| title_short | Periodic solutions for neutral nonlinear differential equations with functional delay |
| title_sort | periodic solutions for neutral nonlinear differential equations with functional delay |
| topic | Krasnoselskii neutral nonlinear integral equation periodic solution unique solution. |
| url | http://ejde.math.txstate.edu/Volumes/2003/102/abstr.html |
| work_keys_str_mv | AT youssefnraffoul periodicsolutionsforneutralnonlineardifferentialequationswithfunctionaldelay |