Banach空间中隐函数和逆函数的整体和半局部定理

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2021-01-01 DOI:10.1070/SM9483

A. Arutyunov, S. Zhukovskiy

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引用次数: 4

摘要

我们考虑两个Banach空间之间的连续映射，这两个空间依赖于拓扑空间中具有值的参数。假设这些映射对于参数的每个值都是连续可微的。在考虑映射的正态性(正则性)假设下，得到了全局隐函数和半局部隐函数存在的充分条件。给出了解的先验估计。作为这些结果的应用，我们得到了隐函数从给定闭集扩展到整个参数空间的定理和映射的重合点定理。参考书目:32种。

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Global and semilocal theorems on implicit and inverse functions in Banach spaces

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.

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis