Nonlinear functional analysis

Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear mappings.

Morse theory is a branch of nonlinear functional analysis.

Topics

Its subject matter includes:^[1]: 1–2

• generalizations of calculus to Banach spaces
• implicit function theorems
• 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 Lusternik–Schnirelmann category theory
• methods of complex function theory

See also

• Functional analysis

Notes

1. Schwartz, Jacob T. (1969). Non-Linear Functional Analysis. New York: Gordon & Breach Science Pub. ISBN 978-0-677-01505-7.