Abstract
This paper is a brief review of results in the theory of covering mappings of metric spaces and vector metric spaces and its applications to implicit differential equations. For the Cauchy problem and boundary-value problems, we obtain existence conditions, estimates of solutions, and conditions of the continuous dependence of solutions on the parameters of the equation and initial and boundary conditions.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 165, Proceedings of the IV International Scientific Conference “Actual Problems of Applied Mathematics,” Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, 2019.
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Burlakov, E.O., Zhukovskaya, T.V., Zhukovskiy, E.S. et al. Applications of Covering Mappings in the Theory of Implicit Differential Equations. J Math Sci 259, 283–295 (2021). https://doi.org/10.1007/s10958-021-05617-7
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DOI: https://doi.org/10.1007/s10958-021-05617-7
Keywords and phrases
- covering mapping
- point of coincidence of mappings
- metric space
- partially ordered space
- implicit differential equation
- Cauchy problem
- boundary-value problem