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Autonomous Noether Boundary-Value Problems not Solved with Respect to the Derivative
- Source :
- Journal of Mathematical Sciences. 230:799-803
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- 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. Poincare, 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 Lienard equation.
- Subjects :
- Statistics and Probability
Lyapunov function
Liénard equation
Applied Mathematics
General Mathematics
010102 general mathematics
01 natural sciences
Constructive
010101 applied mathematics
Nonlinear system
symbols.namesake
Scheme (mathematics)
Poincaré conjecture
symbols
Applied mathematics
Boundary value problem
0101 mathematics
Noether's theorem
Mathematics
Subjects
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 230
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi...........012ebd79498617edf073ef673bbdbef6