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Unbounded solutions and periodic solutions for second order differential equations with asymmetric nonlinearity


Authors: Xiong Li and Ziheng Zhang
Journal: Proc. Amer. Math. Soc. 135 (2007), 2769-2777
MSC (2000): Primary 34C11, 34C25
DOI: https://doi.org/10.1090/S0002-9939-07-08928-9
Published electronically: February 9, 2007
MathSciNet review: 2317951
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we will prove the coexistence of unbounded solutions and periodic solutions for the asymmetric oscillator

$\displaystyle {\ddot x}+f({\dot x})+a x^{+}-bx^{-}=\varphi(t,x), $

where $ a$ and $ b$ are positive constants satisfying the nonresonant condition

$\displaystyle \frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}\notin{\mathbb{Q}} $

and $ \varphi (t,x)$ is $ 2\pi-$periodic in the first variable and bounded.


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Additional Information

Xiong Li
Affiliation: School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People’s Republic of China
Email: xli@bnu.edu.cn

Ziheng Zhang
Affiliation: School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-07-08928-9
Keywords: Unbounded solutions, periodic solutions, asymmetric oscillator.
Received by editor(s): May 4, 2006
Published electronically: February 9, 2007
Additional Notes: This project was supported by the Program for New Century Excellent Talents of Ministry of Education of China and the National Natural Science Foundation of China (Grant No. 10671020 and 10301006)
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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