Nonlinear functional analysis: Difference between revisions

Revision as of 14:44, 17 October 2008

Latest revision as of 07:18, 13 May 2024

(18 intermediate revisions by 12 users not shown)

Line 1:

[[Image:3D-Leveltorus.png|thumb|right|[[Morse theory]] is a branch of nonlinear functional analysis.]]

'''Nonlinear functional analysis''' is a branch of [[mathematical analysis]]. It deals with [[nonlinear]] [[Map (mathematics)|mapping]]s and its subject matter includes:<ref>

{{cite book | last = Schwartz | first = Jacob T. | authorlink = Jack Schwartz | title = Non-Linear Functional Analysis | publisher = Gordon & Breach Science Pub | ___location = New York | year = 1969 | isbn = 9780677015057 }}

'''Nonlinear functional analysis''' is a branch of [[mathematical analysis]]. Itthat deals with [[nonlinear]] [[Map (mathematics)|mapping]]s and its subject matter includes:<ref>.

==Topics==

Its subject matter includes:<ref>

{{cite book | last = Schwartz | first = Jacob T. | authorlink = Jack Schwartz | title = Non-Linear Functional Analysis | publisher = Gordon & Breach Science Pub | ___location = New York | year = 1969 | isbn = 9780677015057978-0-677-01505-7 }}

</ref>{{Rp|1–2}}

* generalizations of [[calculus]] to [[Banach space]]s

* [[implicit function theorem]]s

* fixed-point theorems ([[Brouwer fixed point theorem]], [[Fixed point theorems in infinite-dimensional spaces]], [[topological degree theory]], [[Jordan separation theorem]], [[Lefschetz fixed-point theorem]])

* [[Morse theory]] and [[Lyusternik–SchnirelmannLusternik–Schnirelmann category]] theory

* methods of [[complex function theory]]

==Notes==

<references />

==See also==

* [[Functional analysis]]

==Notes==

{{Mathanalysis-stub}}

{{reflist}}

[[Category:Nonlinear functional analysis]]

{{Authority control}}

[[Category:Nonlinear functional analysis| ]]