Geodesic
Variational approach for weak quasiperiodic solutions of quasiperiodically excited Lagrangian systems on Riemannian manifolds
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 37J45, 34C40, 70H12, 70G75
Keywords: weak quasi periodic solution, natural mechanical system, Riemannian manifold, variational method 
@article{EJDE_2012__2012__a43,
     author = {Parasyuk,  Igor and Rustamova,  Anna},
     title = {Variational approach for weak quasiperiodic solutions of quasiperiodically excited {Lagrangian} systems on {Riemannian} manifolds},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1260.37030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a43/}
}
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%A Rustamova,  Anna
%T Variational approach for weak quasiperiodic solutions of quasiperiodically excited Lagrangian systems on Riemannian manifolds
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a43/
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%F EJDE_2012__2012__a43
Parasyuk,  Igor; Rustamova,  Anna. Variational approach for weak quasiperiodic solutions of quasiperiodically excited Lagrangian systems on Riemannian manifolds. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a43/