An equation in nonlinear combination of iterates

Fuente: arXiv
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Main Authors: Gopalakrishna, Chaitanya, Zhang, Weinian
Format: Preprint
Published: 2024
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author Gopalakrishna, Chaitanya
Zhang, Weinian
author_facet Gopalakrishna, Chaitanya
Zhang, Weinian
contents In this paper we deal with an equation in nonlinear combination of iterates. Although it can be reduced by the logarithm conjugacy to a form for application of Schauder's or Banach's fixed point theorems, a difficulty called Zero Problem is encountered for continuous solutions because the domain does not contain $0$. So we consider solutions with weaker regularity, using the Knaster-Tarski fixed point theorem for complete lattices to give order-preserving solutions. Then we give semi-continuous solutions and integrable solutions.
format Preprint
id arxiv_https___arxiv_org_abs_2401_06420
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle An equation in nonlinear combination of iterates
Gopalakrishna, Chaitanya
Zhang, Weinian
Dynamical Systems
Classical Analysis and ODEs
Rings and Algebras
39B12, 47J05, 06F20
In this paper we deal with an equation in nonlinear combination of iterates. Although it can be reduced by the logarithm conjugacy to a form for application of Schauder's or Banach's fixed point theorems, a difficulty called Zero Problem is encountered for continuous solutions because the domain does not contain $0$. So we consider solutions with weaker regularity, using the Knaster-Tarski fixed point theorem for complete lattices to give order-preserving solutions. Then we give semi-continuous solutions and integrable solutions.
title An equation in nonlinear combination of iterates
topic Dynamical Systems
Classical Analysis and ODEs
Rings and Algebras
39B12, 47J05, 06F20
url https://arxiv.org/abs/2401.06420