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A continuation principle for Fredholm maps I: theory and basics

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  • Christian Pötzsche
  • Robert Skiba

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.

Suggested Citation

  • Christian Pötzsche & Robert Skiba, 2020. "A continuation principle for Fredholm maps I: theory and basics," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 983-1003, May.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:5:p:983-1003
    DOI: 10.1002/mana.201800450
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    Cited by:

    1. Christian Pötzsche & Robert Skiba, 2020. "A continuation principle for Fredholm maps II: application to homoclinic solutions," Mathematische Nachrichten, Wiley Blackwell, vol. 293(6), pages 1174-1199, June.

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