A continuation principle for Fredholm maps I: theory and basics

Christian Pötzsche and Robert Skiba

Mathematische Nachrichten, 2020, vol. 293, issue 5, 983-1003

Abstract: We prove an abstract 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.

Date: 2020
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https://doi.org/10.1002/mana.201800450

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