Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation
In this paper, we prove a uniqueness theorem for rapidly oscillating periodic solutions of the singularly perturbed differential-delay equation $varepsilon dot{x}(t)=-x(t)+f(x(t-1))$. In particular, we show that, for a given oscillation rate, there exists exactly one periodic solution to the above e...
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| Language: | English |
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Texas State University
2000-07-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2000/56/abstr.html |
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doaj-e47600bec99d455e8592b5786b27f6e22020-11-24T20:57:41ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912000-07-01200056118Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equationHari P. KrishnanIn this paper, we prove a uniqueness theorem for rapidly oscillating periodic solutions of the singularly perturbed differential-delay equation $varepsilon dot{x}(t)=-x(t)+f(x(t-1))$. In particular, we show that, for a given oscillation rate, there exists exactly one periodic solution to the above equation. Our proof relies upon a generalization of Lin's method, and is valid under generic conditions. http://ejde.math.txstate.edu/Volumes/2000/56/abstr.htmldelay equationrapidly oscillatingsingularly perturbed. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hari P. Krishnan |
| spellingShingle |
Hari P. Krishnan Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation Electronic Journal of Differential Equations delay equation rapidly oscillating singularly perturbed. |
| author_facet |
Hari P. Krishnan |
| author_sort |
Hari P. Krishnan |
| title |
Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation |
| title_short |
Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation |
| title_full |
Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation |
| title_fullStr |
Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation |
| title_full_unstemmed |
Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation |
| title_sort |
uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2000-07-01 |
| description |
In this paper, we prove a uniqueness theorem for rapidly oscillating periodic solutions of the singularly perturbed differential-delay equation $varepsilon dot{x}(t)=-x(t)+f(x(t-1))$. In particular, we show that, for a given oscillation rate, there exists exactly one periodic solution to the above equation. Our proof relies upon a generalization of Lin's method, and is valid under generic conditions. |
| topic |
delay equation rapidly oscillating singularly perturbed. |
| url |
http://ejde.math.txstate.edu/Volumes/2000/56/abstr.html |
| work_keys_str_mv |
AT haripkrishnan uniquenessofrapidlyoscillatingperiodicsolutionstoasingularlyperturbeddifferentialdelayequation |
| _version_ |
1716787974817972224 |