# Nonlinear functional analysis

```@inproceedings{Browder1970NonlinearFA,
title={Nonlinear functional analysis},
author={Felix Earl Browder},
year={1970}
}```
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…
1,325 Citations
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## References

SHOWING 1-4 OF 4 REFERENCES
An Introduction to Algebraic Topology
A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and
Weak solution, 45, 52 Winding number
• Weak solution, 45, 52 Winding number
Weak solution, 47, 54 Winding number
• Weak solution, 47, 54 Winding number