Article

Full entry | PDF   (0.2 MB)
Keywords:
Lagrangian system; periodic solution
Summary:
A classical mechanics Lagrangian system with even Lagrangian is considered. The configuration space is a cylinder $\mathbb{R}^m\times\mathbb{T}^n$. A large class of nonhomotopic periodic solutions has been found.
References:
[1] Adams R. A., Fournier J. J. F.: Sobolev Spaces. Pure and Applied Mathematics (Amsterdam), 140, Elsevier/Academic Press, Amsterdam, 2003. MR 2424078 | Zbl 1098.46001
[2] Capozzi A., Fortunato D., Salvatore A.: Periodic solutions of Lagrangian systems with bounded potential. J. Math. Anal. Appl. 124 (1987), no. 2, 482–494. DOI 10.1016/0022-247X(87)90009-6 | MR 0887004
[3] Edwards R.: Functional Analysis. Theory and Applications. Holt, Rinehart and Winston, New York, 1965. MR 0221256
[4] Ekeland I., Témam R.: Convex Analysis and Variational Problems. Classics in Applied Mathematics, 28, Society for Industrial and Applied Mathematics, Philadelphia, 1999. MR 1727362
[5] Mawhin J., Willem M.: Critical Point Theory and Hamiltonian Systems. Applied Mathematical Sciences, 74, Springer, New York, 1989. DOI 10.1007/978-1-4757-2061-7 | MR 0982267
[6] Struwe M.: Variational Methods. Applications to Nonlinear partial Differential Equations and Hamiltonian Systems, Results in Mathematics and Related Areas, 3rd Series, A Series of Modern Surveys in Mathematics, 34, Springer, Berlin, 2008. MR 2431434

Partner of