Existence of periodic solutions for second order delay differential equations with impulses
Using the coincidence degree theory by Mawhin, we prove the existence of periodic solutions for the second-order delay differential equations with impulses $displaylines{ x''(t)+f(t,x'(t))+g(x(t-au(t))=p(t),quad tgeq0,; teq t_k,cr Delta x(t_k)=I_k(x(t_k),x'(t_k)),cr Delta x...
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| Format: | Article |
| Language: | English |
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Texas State University
2011-03-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2011/37/abstr.html |
| _version_ | 1819121833102802944 |
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| author | Lijun Pan |
| author_facet | Lijun Pan |
| author_sort | Lijun Pan |
| collection | DOAJ |
| description | Using the coincidence degree theory by Mawhin, we prove the existence of periodic solutions for the second-order delay differential equations with impulses $displaylines{ x''(t)+f(t,x'(t))+g(x(t-au(t))=p(t),quad tgeq0,; teq t_k,cr Delta x(t_k)=I_k(x(t_k),x'(t_k)),cr Delta x'(t_k)=J_k(x(t_k),x'(t_k)). }$$ We obtain new existence results and illustrated them by an example. |
| first_indexed | 2024-12-22T06:42:50Z |
| format | Article |
| id | doaj.art-8cedd6d4d83344fb8520b52c493b6c9a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T06:42:50Z |
| publishDate | 2011-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-8cedd6d4d83344fb8520b52c493b6c9a2022-12-21T18:35:24ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-03-01201137,112Existence of periodic solutions for second order delay differential equations with impulsesLijun PanUsing the coincidence degree theory by Mawhin, we prove the existence of periodic solutions for the second-order delay differential equations with impulses $displaylines{ x''(t)+f(t,x'(t))+g(x(t-au(t))=p(t),quad tgeq0,; teq t_k,cr Delta x(t_k)=I_k(x(t_k),x'(t_k)),cr Delta x'(t_k)=J_k(x(t_k),x'(t_k)). }$$ We obtain new existence results and illustrated them by an example.http://ejde.math.txstate.edu/Volumes/2011/37/abstr.htmlSecond-order delay differential equationsimpulsesperiodic solutioncoincidence degree |
| spellingShingle | Lijun Pan Existence of periodic solutions for second order delay differential equations with impulses Electronic Journal of Differential Equations Second-order delay differential equations impulses periodic solution coincidence degree |
| title | Existence of periodic solutions for second order delay differential equations with impulses |
| title_full | Existence of periodic solutions for second order delay differential equations with impulses |
| title_fullStr | Existence of periodic solutions for second order delay differential equations with impulses |
| title_full_unstemmed | Existence of periodic solutions for second order delay differential equations with impulses |
| title_short | Existence of periodic solutions for second order delay differential equations with impulses |
| title_sort | existence of periodic solutions for second order delay differential equations with impulses |
| topic | Second-order delay differential equations impulses periodic solution coincidence degree |
| url | http://ejde.math.txstate.edu/Volumes/2011/37/abstr.html |
| work_keys_str_mv | AT lijunpan existenceofperiodicsolutionsforsecondorderdelaydifferentialequationswithimpulses |