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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 684962, 10 pages
http://dx.doi.org/10.1155/2013/684962
Research Article

Positive Solutions for Fourth-Order Nonlinear Differential Equation with Integral Boundary Conditions

Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China

Received 5 November 2012; Accepted 8 January 2013

Academic Editor: Cengiz Çinar

Copyright © 2013 Qi Wang 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.

Linked References

  1. X. Hao, L. Liu, and Y. Wu, “Positive solutions for nonlinear nth-order singular nonlocal boundary value problems,” Boundary Value Problems, vol. 2007, Article ID 74517, 10 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. X. Hao, L. Liu, Y. Wu, and Q. Sun, “Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 73, no. 6, pp. 1653–1662, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. R. L. Webb and G. Infante, “Positive solutions of nonlocal boundary value problems: a unified approach,” Journal of the London Mathematical Society, vol. 74, no. 3, pp. 673–693, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. R. Ma and L. Xu, “Existence of positive solutions of a nonlinear fourth-order boundary value problem,” Applied Mathematics Letters, vol. 23, no. 5, pp. 537–543, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Cabada and R. R. Enguiça, “Positive solutions of fourth order problems with clamped beam boundary conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 10, pp. 3112–3122, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. F. Xu, “Three symmetric positive solutions of fourth-order nonlocal boundary value problems,” Electronic Journal of Qualitative Theory of Differential Equations, no. 96, pp. 1–11, 2011. View at MathSciNet
  7. R. Ma and T. Chen, “Existence of positive solutions of fourth-order problems with integral boundary conditions,” Boundary Value Problems, vol. 2011, Article ID 297578, 17 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. Bai, “Positive solutions of some nonlocal fourth-order boundary value problem,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4191–4197, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. R. L. Webb, G. Infante, and D. Franco, “Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions,” Proceedings of the Royal Society of Edinburgh, vol. 138, no. 2, pp. 427–446, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. X. Zhang, M. Feng, and W. Ge, “Existence results for nonlinear boundary-value problems with integral boundary conditions in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 10, pp. 3310–3321, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. X. Zhang and W. Ge, “Positive solutions for a class of boundary-value problems with integral boundary conditions,” Computers & Mathematics with Applications, vol. 58, no. 2, pp. 203–215, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. G. Infante and P. Pietramala, “A cantilever equation with nonlinear boundary conditions,” Electronic Journal of Qualitative Theory of Differential Equations, no. 15, pp. 1–14, 2009. View at Zentralblatt MATH · View at MathSciNet
  13. P. Pietramala, “A note on a beam equation with nonlinear boundary conditions,” Boundary Value Problems, vol. 2011, Article ID 376782, 14 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. R. L. Webb and G. Infante, “Non-local boundary value problems of arbitrary order,” Journal of the London Mathematical Society, vol. 79, no. 1, pp. 238–258, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. R. L. Webb and G. Infante, “Semi-positone nonlocal boundary value problems of arbitrary order,” Communications on Pure and Applied Analysis, vol. 9, no. 2, pp. 563–581, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. M. A. Krasnoselśkiĭ, Positive Solutions of Operator Equations, P. Noordhoff, Groningen, The Netherlands, 1964. View at MathSciNet