Quasi-periodic solutions for beam equations with the nonlinear terms depending on the space variable |
| |
| Authors: | Yi Wang Jianguo Si |
| |
| Affiliation: | 1. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong, People's Republic of China yiwang8080@126.com;3. School of Mathematics, Shandong University, Jinan, Shandong, People's Republic of China |
| |
| Abstract: | ABSTRACT This article is devoted to the study of a beam equation with an x-dependent nonlinear term. We construct an analytic and symplectic transformation which changes the Hamiltonian to its Birkhoff normal form. However, the infinitely many coefficients of the Hamiltonian generating this transformation have small denominators. We prove that these denominators do not vanish for all indices and the transformation is canonical. Applying the normal form to a KAM theorem, it is proved that the equation admits quasi-periodic solutions with prescribed frequencies for any fixed potential constant. |
| |
| Keywords: | Rolando Magnanini |
|
|
