An equation in nonlinear combination of iterates
Dynamical Systems
2024-01-15 v1 Classical Analysis and ODEs
Rings and Algebras
Abstract
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 . 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.
Cite
@article{arxiv.2401.06420,
title = {An equation in nonlinear combination of iterates},
author = {Chaitanya Gopalakrishna and Weinian Zhang},
journal= {arXiv preprint arXiv:2401.06420},
year = {2024}
}
Comments
22 pages. arXiv admin note: text overlap with arXiv:2105.03379