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2022 Boundedness in Asymmetric Oscillations at Resonance in a Critical Situation
Shufang Zhang, Xinli Zhang
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Taiwanese J. Math. Advance Publication 1-16 (2022). DOI: 10.11650/tjm/220404

Abstract

In this article, by using Moser's twist theorem, we prove that all solutions of the equation $x'' + ax^{+} - bx^{-} + \varphi(x) = p(t)$ are bounded in the critical situation, where $p$ is a smooth periodic function, and $\varphi$ is bounded one.

Funding Statement

This work was supported by the NSFC (grant no. 11801295).

Acknowledgments

The authors are grateful to the referees for their valuable suggestions and comments.

Citation

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Shufang Zhang. Xinli Zhang. "Boundedness in Asymmetric Oscillations at Resonance in a Critical Situation." Taiwanese J. Math. Advance Publication 1 - 16, 2022. https://doi.org/10.11650/tjm/220404

Information

Published: 2022
First available in Project Euclid: 26 April 2022

Digital Object Identifier: 10.11650/tjm/220404

Subjects:
Primary: 34C11 , 34C27 , 37E40

Keywords: asymmetric oscillations , at resonance , boundedness , critical situation , twist theorem

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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