Guiding Potentials and Bounded Solutions of Differential Equations on Finite-Dimensional Non-Compact Manifolds
Yu. E. Gliklikh · Russian Mathematics · 2021
The paper is devoted to some modification of the theory of guiding potentials in such a way that it becomes applicable to investigation of ordinary differential equations on finite-dimensional non-compact smooth manifolds. Two constructions of the topological index on manifolds are described―for the maps of manifolds and for tangent and cotangent vector fields. On the basis of this modification we prove a theorem of existence of a solution that is uniformly bounded on the entire line.