A continuation principle for Fredholm maps I: theory and basics

We prove an and flexible continuation theorem for zeros of parametrized Fredholm maps between Banach spaces. It guarantees not only the existence of zeros to corresponding equations, but also that they form a continuum for parameters from a connected manifold. Our basic tools are transfer maps and a...

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Bibliographic Details
Published in:Mathematische Nachrichten 2020-05, Vol.293 (5), p.983-1003
Main Authors: Pötzsche, Christian, Skiba, Robert
Format: Article
Language:English
Subjects:
Banach spaces
Boundary value problems
Fredholm operator
properness
topological degree
transfer map
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Summary:We prove an and flexible continuation theorem for zeros of parametrized Fredholm maps between Banach spaces. It guarantees not only the existence of zeros to corresponding equations, but also that they form a continuum for parameters from a connected manifold. Our basic tools are transfer maps and a specific topological degree. The main result is tailor‐made to solve boundary value problems over infinite time‐intervals and for the (global) continuation of homoclinic solutions.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201800450