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A continuation principle for Fredholm maps I: theory and basics
Author(s) -
Pötzsche Christian,
Skiba Robert
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800450
Subject(s) - mathematics , continuation , banach space , fredholm integral equation , manifold (fluid mechanics) , fredholm theory , mathematical analysis , pure mathematics , integral equation , computer science , mechanical engineering , engineering , programming language
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.