Asymptotic Expansions of Eigenvalues of Periodic and Antiperiodic Boundary Problems for Singularly Perturbed Second Order Differential Equation with Turning Points
For a second order equation with a small factor at the highest derivative the asymptotic behavior of all eigenvalues of periodic and antiperiodic problems is studied. The main assumption is that the coefficient at the first derivative in the equation is the sign of the variable so that turning points e...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Yaroslavl State University
2016-02-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/306 |
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| Summary: | For a second order equation with a small factor at the highest derivative the asymptotic behavior of all eigenvalues of periodic and antiperiodic problems is studied. The main assumption is that the coefficient at the first derivative in the equation is the sign of the variable so that turning points exist an algorithm for computing all coefficients of asymptotic series for every considered eigenvalue is developed. It turns out that the values of these coefficients are defined by coefficient values of the original equation only in a neighborhood of turning points. Asymptotics for the length of Lyapunov zones of stability and instability was obtained. In particular, the problem of stability of solutions of second order equations with periodic coefficients and small parameter at the highest derivative was solved |
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| ISSN: | 1818-1015 2313-5417 |