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Guiding Potentials and Bounded Solutions of Differential Equations on Finite-Dimensional Non-Compact Manifolds

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Abstract

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.

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REFERENCES

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Funding

This work was funded by the Russian Foundation for Basic Research, grant no. 18-01-00048.

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Authors and Affiliations

  1. Voronezh State University, 1 Universitetskaya sq., 394018, Voronezh, Russia

    Yu. E. Gliklikh

  2. I.A. Bunin Yelets State University, 28 Kommunarov str., 399770, Yelets, Russia

    Yu. E. Gliklikh

Authors
  1. Yu. E. Gliklikh
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Correspondence to Yu. E. Gliklikh.

Additional information

Dedicated to 90th anniversary of the birth of my teacher Prof. Yu.G.Borisovich

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 5, pp. 16–22.

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Gliklikh, Y.E. Guiding Potentials and Bounded Solutions of Differential Equations on Finite-Dimensional Non-Compact Manifolds. Russ Math. 65, 8–12 (2021). https://doi.org/10.3103/S1066369X21050030

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  • DOI: https://doi.org/10.3103/S1066369X21050030

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