Qiuju Tuo, Jianguo Si
Abstract:
In this article, we consider the one-dimensional nonlinear beam
equations with quasi-periodic quintic nonlinearities
under periodic boundary conditions, where B is a positive constant,
is a small positive parameter,
is a real analytic
quasi-periodic function in t with frequency vector
.
It is proved that the above equation admits many quasi-periodic solutions
by KAM theory and partial Birkhoff normal form.
Submitted October 24, 2014. Published January 7, 2015.
Math Subject Classifications: 35L05, 37K50, 58E05.
Key Words: Infinite dimensional Hamiltonian systems; KAM theory;
beam equations; quasi-periodic solutions; invariant torus.
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Qiuju Tuo School of Mathematics, Shandong University Jinan, Shandong 250100, China email: qiujutuo@163.com | |
Jianguo Si School of Mathematics, Shandong University Jinan, Shandong 250100, China email: sijgmath@sdu.edu.cn |
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