Topic
Nonlinear functional analysis
About: Nonlinear functional analysis is a research topic. Over the lifetime, 240 publications have been published within this topic receiving 29936 citations.
Papers published on a yearly basis
Papers
Book•
1 Oct 1984
TL;DR: A survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis can be found in this article, with extensive commentary, many examples, and interesting, challenging exercises.
Abstract: This graduate-level text offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It features extensive commentary, many examples, and interesting, challenging exercises. Topics include degree mappings for infinite dimensional spaces, the inverse function theory, the implicit function theory, Newton's methods, and many other subjects. 1985 edition.
5,319 citations
1 Mar 1988
4,893 citations
1 Jan 1970
TL;DR: In this paper, a brief introduction to nonlinear functional analysis in Banach spaces is provided, with a brief discussion of monotone operators and their applications to game theory, integral equations, and ordinary differential equations.
Abstract: This manuscript provides a brief introduction to nonlinear functional analysis. We start out with calculus in Banach spaces, review differentiation and integration, derive the implicit function theorem (using the uniform contraction principle) and apply the result to prove existence and uniqueness of solutions for ordinary differential equations in Banach spaces. Next we introduce the mapping degree in both finite (Brouwer degree) and infinite dimensional (Leray-Schauder degree) Banach spaces. Several applications to game theory, integral equations, and ordinary differential equations are discussed. As an application we consider partial differential equations and prove existence and uniqueness for solutions of the stationary Navier-Stokes equation. Finally, we give a brief discussion of monotone operators.
2,182 citations
TL;DR: A survey of nonlinear functional analysis in ordered Banach spaces can be found in this paper, where some of the most important methods and results of non-linear functional analyses are discussed.
Abstract: This paper gives a survey over some of the most important methods and results of nonlinear functional analysis in ordered Banach spaces. By means of iterative techniques and by using topological to...
1,997 citations
Book•
11 Dec 1989
1,982 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 16 |
| 2020 | 8 |
| 2019 | 5 |
| 2018 | 10 |
| 2017 | 4 |
| 2016 | 5 |