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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| Format: | Article |
| Language: | English |
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Texas State University
2000-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2000/56/abstr.html |
| _version_ | 1818369089903525888 |
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| author | Hari P. Krishnan |
| author_facet | Hari P. Krishnan |
| author_sort | Hari P. Krishnan |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-13T23:18:18Z |
| format | Article |
| id | doaj.art-e47600bec99d455e8592b5786b27f6e2 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-13T23:18:18Z |
| publishDate | 2000-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-e47600bec99d455e8592b5786b27f6e22022-12-21T23:27:52ZengTexas 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. |
| 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. |
| title | 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_short | 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 |
| 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 |