Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 116, pp. 1-11.

Title: Periodic solutions for second order delay Duffing
       equation via critical point theory
        
Authors: Jingrui Zhang (Beijing Institute of Technology, China)
         Yi Cheng      (Aviation Univ., Changchun, China)
         Changqin Yuan (Aviation Univ., Changchun, China)

Abstract:
 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 06, 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This article was withdrawn by the authors on July 21, 2013.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"