Autonomous Noether Boundary-Value Problems not Solved with Respect to the Derivative
- Autores: Chuiko S.1, Nesmelova (Starkova) O.2
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Afiliações:
- Donbass State Pedagogical University
- Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine
- Edição: Volume 230, Nº 5 (2018)
- Páginas: 799-803
- Seção: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/240988
- DOI: https://doi.org/10.1007/s10958-018-3793-1
- ID: 240988
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Resumo
In monographs of N. V. Azbelev, A. M. Samoilenko, and A. A. Boichuk, constructive methods of study of Noether boundary-value problems have been developed. These methods continue the investigation of periodic problems stated by H. Poincaré, A. M. Lyapunov, N. M. Krylov, N. N. Bogolyubov, I. G. Malkin, and O. Veivoda by the methods of small parameter. We propose an improved scheme of study of autonomous Noether boundary-value problems for nonlinear systems in critical cases. In the case of multiple roots of the equation for generating constants, we obtain sufficient conditions of existence of solutions to an autonomous boundary-value problem not solved with respect to the derivative. The effectiveness of the scheme proposed is illustrated by an example of the periodic problem for the Liénard equation.
Sobre autores
S. Chuiko
Donbass State Pedagogical University
Autor responsável pela correspondência
Email: chujko-slav@inbox.ru
Ucrânia, Slavyansk
O. Nesmelova (Starkova)
Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine
Email: chujko-slav@inbox.ru
Ucrânia, Slavyansk