Differential Equations

, Volume 55, Issue 4, pp 437–448 | Cite as

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

  • A. V. ArutyunovEmail author
  • S. E. ZhukovskiyEmail author
Ordinary Differential Equations


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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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.RUDN UniversityMoscowRussia
  2. 2.Trapeznikov Institute of Control Sciences of the Russian Academy of SciencesMoscowRussia
  3. 3.Derzhavin Tambov State UniversityTambovRussia
  4. 4.Moscow Institute of Physics and Technology (State University)DolgoprudnyiRussia
  5. 5.Institute for Information Transmission Problems of the Russian Academy of SciencesMoscowRussia

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