Abstract
This chapter deals with the local inversion theorem and the implicit function theorem in Banach spaces. The Lyapunov—Schmidt reduction is discussed in Section 3.3. In Section 3.4 we prove the global inversion theorem, which goes back to Hadamard and Caccioppoli. Section 3.5 deals with a global inversion theorem in the presence of fold singularities.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Ambrosetti, A., Arcoya, D. (2011). Local and Global Inversion Theorems. In: An Introduction to Nonlinear Functional Analysis and Elliptic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 82. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8114-2_3
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8114-2_3
Published:
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-8113-5
Online ISBN: 978-0-8176-8114-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)