Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 454658, 7 pages
http://dx.doi.org/10.1155/2014/454658
Research Article

The Solvability and Numerical Simulation for the Elastic Beam Problems with Nonlinear Boundary Conditions

School of Business, Shandong University of Technology, Zibo 255049, China

Received 24 April 2014; Accepted 12 May 2014; Published 22 May 2014

Academic Editor: Juntao Sun

Copyright © 2014 Qun Gao. 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. E. Alves, T. F. Ma, and M. L. Pelicer, “Monotone positive solutions for a fourth order equation with nonlinear boundary conditions,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 9, pp. 3834–3841, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. T.F. Ma, “Positive solutions for a beam equation on a nonlinear elastic foundation,” Mathematical and Computer Modelling, vol. 39, no. 11-12, pp. 1195–1201, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. G. Bonanno and B. Di Bella, “A boundary value problem for fourth-order elastic beam equations,” Journal of Mathematical Analysis and Applications, vol. 343, no. 2, pp. 1166–1176, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. G. Bonanno and B. Di Bella, “Infinitely many solutions for a fourth-order elastic beam equation,” Nonlinear Differential Equations and Applications, vol. 18, no. 3, pp. 357–368, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. G. Han and Z. Xu, “Multiple solutions of some nonlinear fourth-order beam equations,” Nonlinear Analysis: Theory, Methods and Applications, vol. 68, no. 12, pp. 3646–3656, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. X.-L. Liu and W.-T. Li, “Existence and multiplicity of solutions for fourth-order boundary value problems with parameters,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 362–375, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. T. F. Ma, “Existence results and numerical solutions for a beam equation with nonlinear boundary conditions,” Applied Numerical Mathematics, vol. 47, no. 2, pp. 189–196, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. L. Yang, H. Chen, and X. Yang, “The multiplicity of solutions for fourth-order equations generated from a boundary condition,” Applied Mathematics Letters, vol. 24, no. 9, pp. 1599–1603, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. F. Li and J. Sun, “Infinitely many homoclinic solutions for a nonperiodic fourth-order differential equation without (AR)-condition,” Applied Mathematics and Compution. In press.
  10. H. Chen and J. Sun, “An application of variational method to second-order impulsive differential equation on the half-line,” Applied Mathematics and Computation, vol. 217, no. 5, pp. 1863–1869, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. J. R. Graef, S. Heidarkhani, and L. Kong, “A variational approach to a Kirchhoff-type problem involving two parameters,” Results in Mathematics, vol. 63, pp. 877–889, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. B. Ricceri, “On an elliptic Kirchhoff-type problem depending on two parameters,” Journal of Global Optimization, vol. 46, no. 4, pp. 543–549, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. J. Sun, H. Chen, J. J. Nieto, and M. Otero-Novoa, “The multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects,” Nonlinear Analysis: Theory, Methods and Applications, vol. 72, no. 12, pp. 4575–4586, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. B. Ricceri, “A further three critical points theorem,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 9, pp. 4151–4157, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. B. Ricceri, “A three critical points theorem revisited,” Nonlinear Analysis: Theory, Methods and Applications, vol. 70, no. 9, pp. 3084–3089, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. B. Ricceri, “Existence of three solutions for a class of elliptic eigenvalue problems,” Mathematical and Computer Modelling, vol. 32, no. 11–13, pp. 1485–1494, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. E. Zeidler, Nonlinear Functional Analysis and Its Applications, Springer, Berlin, Germany, 1990.