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Application of Methods of Ordinary Differential Equations to Global Inverse Function Theorems

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Abstract

We obtain a global inverse function theorem guaranteeing that if a smooth mapping of finite-dimensional spaces is uniformly nonsingular, then it has a smooth right inverse. Global implicit function theorems are obtained guaranteeing the existence and continuity of a global implicit function under the condition that the mappings in question are uniformly nonsingular. The local Lipschitz property and the smoothness of the global implicit function are studied. The results are generalized to the case of mappings of Hilbert spaces.

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Authors and Affiliations

  1. RUDN University, Moscow, 117198, Russia

    A. V. Arutyunov & S. E. Zhukovskiy

  2. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Moscow, 117997, Russia

    A. V. Arutyunov & S. E. Zhukovskiy

  3. Derzhavin Tambov State University, Tambov, 392000, Russia

    A. V. Arutyunov

  4. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, 141701, Russia

    A. V. Arutyunov & S. E. Zhukovskiy

  5. Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, 127051, Russia

    A. V. Arutyunov

Authors
  1. A. V. Arutyunov
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  2. S. E. Zhukovskiy
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Correspondence to A. V. Arutyunov or S. E. Zhukovskiy.

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Arutyunov, A.V., Zhukovskiy, S.E. Application of Methods of Ordinary Differential Equations to Global Inverse Function Theorems. Diff Equat 55, 437–448 (2019). https://doi.org/10.1134/S0012266119040013

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  • DOI: https://doi.org/10.1134/S0012266119040013

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