In this paper we study ordinary differential equations on a noncomplete Riemannian manifold. Using the Ljusternik-Schnirelmann theory, we prove the existence of infinitely many solutions joining two given submanifolds.
Addolorata Salvatore. "Trajectories of dynamical systems joining two given submanifolds." Differential Integral Equations 9 (4) 779 - 790, 1996. https://doi.org/10.57262/die/1367969887