Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 66, pp. 1-22.

Title: Variational approach for weak quasiperiodic solutions
       of quasiperiodically excited Lagrangian systems
       on Riemannian manifolds

Authors: Igor Parasyuk (National Taras Shevchenko Univ., Kyiv, Ukraine)
         Anna Rustamova (National Taras Shevchenko Univ., Kyiv, Ukraine)

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 02, 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.