Geodesic
Guiding Potentials and bounded solutions of differential equations on finite-dimensional non-compact maniforlds
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 16-22

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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 non-compact 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.
Keywords: non-compact finite-dimensional manifold, vector field and differential equation, guiding potential, uniformly bounded solution. 
@article{IVM_2021_5_a3,
     author = {Yu. E. Gliklikh},
     title = {Guiding {Potentials} and bounded solutions of differential equations on finite-dimensional non-compact maniforlds},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {16--22},
     publisher = {mathdoc},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_5_a3/}
}
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Yu. E. Gliklikh. Guiding Potentials and bounded solutions of differential equations on finite-dimensional non-compact maniforlds. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 16-22. http://geodesic.mathdoc.fr/item/IVM_2021_5_a3/