Existence of bounded asymptotic solutions of autonomous differential equations

Authors

• Minh Van Nguyen Dr., UA Little Rock, Department of Mathematics and StatisticsFollow
• Vu Trong Luong, Vietnam National University at Hanoi
• William Barker, University of Arkansas at Little Rock
• DucHuy Nguyen, Vietnam National University at Hanoi

Document Type

Article

Publication Title

Journal of Differential Equations 434 (2025)

Abstract

We study the existence of bounded asymptotic mild solutions to evolution equations of the form u′(t)=Au(t)+f(t),t≥0in a Banach space X, where Agenerates an (analytic) C0-semigroup and fis bounded. We fifind spectral conditions on Aand ffor the existence and uniqueness of asymptotic mild solutions with the same as that of f. In the resonance case, a sufficient condition of Massera type theorem is found for the existence of bounded solutions with the same profifile as f. The obtained results are stated in terms of spectral properties of Aand f, and they are analogs of classical results of Katznelson-Tzafriri and Massera for the evolution equations on the half line. Applications from PDE are given. ©2025 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). MSC: primary 34G10; secondary 34C25, 34D05

Department

Mathematics and Statistics

DOI

https://doi.org/10.1016/j.jde.2025.113320.

Publication Date

4-15-2025

Recommended Citation

Nguyen, Minh Van Dr.; Luong, Vu Trong; Barker, William; and Nguyen, DucHuy, "Existence of bounded asymptotic solutions of autonomous differential equations" (2025). Journal of Differential Equations ScholarHub@UALittleRock https://doi.org/10.1016/j.jde.2025.113320.