Autonomous Noether Boundary-Value Problems not Solved with Respect to the Derivative

Journal Article · Tue May 15 04:00:00 EDT 2018 · Journal of Mathematical Sciences

DOI:https://doi.org/10.1007/S10958-018-3793-1· OSTI ID:22771264

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.

• OSTI ID: 22771264
• Journal Information: Journal of Mathematical Sciences, Journal Name: Journal of Mathematical Sciences Journal Issue: 5 Vol. 230; ISSN JMTSEW; ISSN 1072-3374
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
BOUNDARY-VALUE PROBLEMS
DIFFERENTIAL EQUATIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PERIODICITY