Abstract
For nonlinear mappings acting in Banach spaces, we examine inverse and implicit function theorems under various smoothness assumptions. For various regularity (normality) conditions imposed on such mappings, we prove that the corresponding equations have solutions under any sufficiently small (in the norm) completely continuous perturbations. A priori estimates for these solutions are obtained.
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Funding
This work was supported by the Volkswagen Foundation. The research presented in Section 2 was performed by the second author and supported by the Russian Science Foundation under grant 20-11-20131.
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Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 312, pp. 7–21 https://doi.org/10.4213/tm4149.
Translated by I. Nikitin
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Arutyunov, A.V., Zhukovskiy, S.E. Stable Solvability of Nonlinear Equations under Completely Continuous Perturbations. Proc. Steklov Inst. Math. 312, 1–15 (2021). https://doi.org/10.1134/S0081543821010016
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DOI: https://doi.org/10.1134/S0081543821010016