Geodesic
Variational approach for weak quasiperiodic solutions of quasiperiodically excited Lagrangian systems on Riemannian manifolds
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a43/}
}
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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/