<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We provide two sufficient criteria for the bifurcation of bounded entire or homoclinic solutions to nonautonomous difference equations depending on a single real parameter. Our analysis is based on a nonhyperbolic solution, whose variational equation possesses exponential dichotomies on semiaxes ensuring that the corresponding critical spectral interval of the dichotomy spectrum has strict multiplicity > 1. This extends earlier results on the fold bifurcation.</p>
</abstract>

We provide two sufficient criteria for the bifurcation of bounded entire or homoclinic solutions to nonautonomous difference equations depending on a single real parameter. Our analysis is based on a nonhyperbolic solution, whose variational equation possesses exponential dichotomies on semiaxes ensuring that the corresponding critical spectral interval of the dichotomy spectrum has strict multiplicity > 1. This extends earlier results on the fold bifurcation.

Nonautonomous Fold Bifurcations from Spectral Intervals of Higher Strict Multiplicity

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

We provide two sufficient criteria for the bifurcation of bounded entire or homoclinic solutions to nonautonomous difference equations depending on a single...

Nonautonomous Fold Bifurcations from Spectral Intervals of Higher Strict Multiplicity

Published Online: Jun 28, 2023

Page range: 87 - 110

Received: Nov 07, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0018

Keywords
nonautonomous bifurcation, nonautonomous difference equation, Fredholm operator, entire solution, dichotomy spectrum

© 2023 Christian Pötzsche, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Nonautonomous Fold Bifurcations from Spectral Intervals of Higher Strict Multiplicity

Published Online: Jun 28, 2023

Page range: 87 - 110

Received: Nov 07, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0018

Keywordsnonautonomous bifurcation, nonautonomous difference equation, Fredholm operator, entire solution, dichotomy spectrum

© 2023 Christian Pötzsche, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
nonautonomous bifurcation, nonautonomous difference equation, Fredholm operator, entire solution, dichotomy spectrum