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Abstract and Applied Analysis
Volume 2014, Article ID 649270, 15 pages
Research Article

Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms

1School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China
2Key Laboratory of Symbolic Computation and Knowledge Engineering, Ministry of Education, Jilin University, Changchun, Jilin 130012, China
3Fundamental Department, Aviation University of Air Force, Changchun 130023, China

Received 28 February 2014; Revised 25 April 2014; Accepted 28 April 2014; Published 18 May 2014

Academic Editor: Yongli Song

Copyright © 2014 Yixian Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the existence of quasiperiodic solutions with two frequencies of completely resonant, quasiperiodically forced nonlinear wave equations subject to periodic spatial boundary conditions. The solutions turn out to be, at the first order, the superposition of traveling waves, traveling in the opposite or the same directions. The proofs are based on the variational Lyapunov-Schmidt reduction and the linking theorem, while the bifurcation equations are solved by variational methods.