Geodesic
Global and semilocal theorems on implicit and inverse functions in Banach spaces
Sbornik. Mathematics, Tome 213 (2022) no. 1, pp. 1-41 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider continuous mappings between two Banach spaces that depend on a parameter with values in a topological space. These mappings are assumed to be continuously differentiable for each value of the parameter. Under normality (regularity) assumptions of the mappings under consideration, we obtain sufficient conditions for the existence of global and semilocal implicit functions. A priori estimates for solutions are given. As an application of these results, we obtain, in particular, a theorem on extending an implicit function from a given closed set to the whole parameter space and a theorem on coincidence points of mappings. Bibliography: 32 titles.
Keywords: global implicit function, semilocal implicit function, global inversion function theorem, normality condition, continuous extension of an implicit function. 
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A. V. Arutyunov; S. E. Zhukovskiy. Global and semilocal theorems on implicit and inverse functions in Banach spaces. Sbornik. Mathematics, Tome 213 (2022) no. 1, pp. 1-41. http://geodesic.mathdoc.fr/item/SM_2022_213_1_a0/

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