Electron. J. Diff. Equ., Vol. 2013 (2013), No. 116, pp. 1-11.

Periodic solutions for second order delay Duffing equation via critical point theory

Jingrui Zhang, Yi Cheng, Changqin Yuan

This article concerns the periodic problem of second order delay Duffing equation with cross resonance condition. Using critical point theory and homotopy methods, we obtain sufficient conditions for the existence of periodic solutions. Also, we present an example to illustrate our results.

Submitted January 12, 2013. Published May 6, 2013.
Math Subject Classifications: 34C25, 34B15.
Key Words: Periodic solution; critical point theory; Duffing equation.

This article was withdrawn by the authors on July 21, 2013.
"We found some fatal errors in the proof of section 3, so that many structural proofs are wrong. According to academic rigor, we think it is not suitable for publication. So we decided to withdraw our paper"

Jingrui Zhang
School of Aerospace Engineering
Beijing Institute of Technology
Beijing, 100081, China
email: ruierchat@yahoo.com.cn
Yi Cheng
Fundamental Department, Aviation University of Air Force
Changchun 130022, China.
Institute of Mathematics, Jilin University
Changchun, 130012, China
email: chengyi407@126.com
Changqin Yuan
Fundamental Department
Aviation University of Air Force
Changchun, 130022, China
email: ycq02@mails.tsinghua.edu.cn

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