Igor Parasyuk, Anna Rustamova
Abstract:
We apply a variational method to prove the existence of weak Besicovitch
quasiperiodic solutions for natural Lagrangian system on Riemannian manifold
with time-quasiperiodic force function. In contrast to previous papers, our
approach does not require non-positiveness condition for sectional Riemannian
curvature. As an application of obtained results, we find conditions for the
existence of weak quasiperiodic solutions in spherical pendulum system under
quasiperiodic forcing.
Submitted March 1, 2012. Published May 2, 2012.
Math Subject Classifications: 37J45, 34C40, 70H12, 70G75.
Key Words: Weak quasi periodic solution; natural mechanical system;
Riemannian manifold; variational method.
An addendum was attached on December 28, 2012. It presents a stronger result concerning the convergence of minimizing sequence to weak quasiperiodic solution. It also corrects a few misprints. See the last 5 pages of this article.
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Igor Parasyuk National Taras Shevchenko University of Kyiv Faculty of Mechanics and Mathematics Volodymyrs'ka 64/13, Kyiv, 01601, Ukraine email: pio@mail.univ.kiev.ua |
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Anna Rustamova National Taras Shevchenko University of Kyiv Faculty of Mechanics and Mathematics Volodymyrs'ka 64/13, Kyiv, 01601, Ukraine email: anna_rustamova@hotmail.com |
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