Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 253532, 8 pages
http://dx.doi.org/10.1155/2014/253532
Research Article

Strong Pullback Attractors for Nonautonomous Suspension Bridge Equations

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China

Received 1 December 2013; Accepted 8 January 2014; Published 9 March 2014

Academic Editors: F. Ding and C.-H. Lien

Copyright © 2014 Wenchao Ju and Xuan Wang. 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.

Linked References

  1. A. C. Lazer and P. J. Mckenna, “Large-amplitude periodic oscillations in suspension bridges. Some new connections with nonlinear analysis,” SIAM Review, vol. 32, no. 4, pp. 537–578, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. Y. K. An, On the suspension bridge equations and the relevant problems [Ph.D. thesis], 2001.
  3. Y. An and C. Zhong, “Periodic solutions of a nonlinear suspension bridge equation with damping and nonconstant load,” Journal of Mathematical Analysis and Applications, vol. 279, no. 2, pp. 569–579, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. Q. H. Choi and T. Jung, “A nonlinear suspension bridge equation with nonconstant load,” Nonlinear Analysis: Theory, Methods & Applications, vol. 35, no. 6, pp. 649–668, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. L. D. Humphreys, “Numerical mountain pass solutions of a suspension bridge equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 28, no. 11, pp. 1811–1826, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. A. C. Lazer and P. J. McKenna, “Large scale oscillatory behavior in asymmetric systems,” Annales de l'Institut Henri Poincaré C, vol. 4, pp. 243–274, 1987. View at Google Scholar
  7. P. J. McKenna and W. Walter, “Nonlinear oscillations in a suspension bridge,” Archive for Rational Mechanics and Analysis, vol. 98, no. 2, pp. 167–177, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. Q. Z. Ma and C. K. Zhong, “Existence of global attractors for the coupled system of suspension bridge equations,” Journal of Mathematical Analysis and Applications, vol. 308, no. 1, pp. 365–379, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. Q. Z. Ma and C. K. Zhong, “Existence of global attractors for the suspension bridge equations,” Journal of Sichuan University, vol. 43, no. 2, pp. 271–276, 2006. View at Google Scholar · View at MathSciNet
  10. C. K. Zhong, Q. Z. Ma, and C. Y. Sun, “Existence of strong solutions and global attractors for the suspension bridge equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 2, pp. 442–454, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. T. Caraballo, G. Łukaszewicz, and J. Real, “Pullback attractors for asymptotically compact non-autonomous dynamical systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 3, pp. 484–498, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. J. Y. Park and J. R. Kang, “Pullback 𝒟-attractors for non-autonomous suspension bridge equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 10, pp. 4618–4623, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. J. R. Kang, “Pullback attractors for the non-autonomous coupled suspension bridge equations,” Applied Mathematics and Computation, vol. 219, no. 16, pp. 8747–8758, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  14. Y. H. Wang and C. K. Zhong, “Pullback 𝒟-attractors for nonautonomous sine-Gordon equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 7, pp. 2137–2148, 2007. View at Publisher · View at Google Scholar · View at Scopus