Quasiperiodic Extremals of Nonautonomous Lagrangian Systems on Riemannian Manifolds
The paper deals with a quasiperiodically excited natural Lagrangian system on a Riemannian manifold. We find sufficient conditions under which this system has a weak Besicovitch quasiperiodic solution minimizing the averaged Lagrangian. It is proved that this solution is indeed a twice continuously differentiable uniformly quasiperiodic function, and the corresponding system in variations is exponentially dichotomous on the real axis.
English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 10, pp 1553-1574.
Citation Example: Parasyuk I. O. Quasiperiodic Extremals of Nonautonomous Lagrangian Systems on Riemannian Manifolds // Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1387–1406.