About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 614376, 7 pages
http://dx.doi.org/10.1155/2014/614376
Research Article

Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem

Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050, China

Received 11 November 2013; Revised 14 December 2013; Accepted 16 December 2013; Published 8 January 2014

Academic Editor: Gabriele Bonanno

Copyright © 2014 Wenguo Shen and Tao He. 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. R. P. Agarwal and Y. M. Chow, “Iterative methods for a fourth order boundary value problem,” Journal of Computational and Applied Mathematics, vol. 10, no. 2, pp. 203–217, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. R. Ma and H. P. Wu, “Positive solutions of a fourth-order two-point boundary value problem,” Acta Mathematica Scientia A, vol. 22, no. 2, pp. 244–249, 2002.
  3. Q. Yao, “Multiple positive solutions to a singular beam equation fixed at both ends,” Acta Mathematica Scientia A, vol. 28, no. 4, pp. 768–778, 2008.
  4. Q. Yao, “Positive solutions for eigenvalue problems of fourth-order elastic beam equations,” Applied Mathematics Letters, vol. 17, no. 2, pp. 237–243, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. B. P. Rynne, “Infinitely many solutions of superlinear fourth order boundary value problems,” Topological Methods in Nonlinear Analysis, vol. 19, no. 2, pp. 303–312, 2002.
  6. P. Korman, “Uniqueness and exact multiplicity of solutions for a class of fourth-order semilinear problems,” Proceedings of the Royal Society of Edinburgh A, vol. 134, no. 1, pp. 179–190, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. J. Xu and X. Han, “Nodal solutions for a fourth-order two-Ooint boundary value problem,” Boundary Value Problem, vol. 2010, Article ID 570932, 11 pages, 2010. View at Publisher · View at Google Scholar
  8. W. G. Shen, “Existence of nodal solutions of a nonlinear fourth-order two-point boundary value problem,” Boundary Value Problems, vol. 2012, p. 31, 2012. View at Publisher · View at Google Scholar
  9. W. G. Shen, “Global structure of nodal solutions for a fourth-order two-point boundary value problem,” Applied Mathematics and Computation, vol. 219, no. 1, pp. 88–98, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. 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 Section A, vol. 138, no. 2, pp. 427–446, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. R. Ma and Y. An, “Global structure of positive solutions for superlinear second order m-point boundary value problems,” Topological Methods in Nonlinear Analysis, vol. 34, no. 2, pp. 279–290, 2009. View at Zentralblatt MATH · View at Scopus
  12. R. Ma, “Nodal solutions for a fourth-order two-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 314, no. 1, pp. 254–265, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. R. Ma, “Nodal solutions of boundary value problems of fourth-order ordinary differential equations,” Journal of Mathematical Analysis and Applications, vol. 319, no. 2, pp. 424–434, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. R. Ma and J. Xu, “Bifurcation from interval and positive solutions of a nonlinear fourth-order boundary value problem,” Nonlinear Analysis, Theory, Methods and Applications, vol. 72, no. 1, pp. 113–122, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. R. Ma, “Existence of positive solutions of a fourth-order boundary value problem,” Applied Mathematics and Computation, vol. 168, no. 2, pp. 1219–1231, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. Z. Bai and H. Wang, “On positive solutions of some nonlinear fourth-order beam equations,” Journal of Mathematical Analysis and Applications, vol. 270, no. 2, pp. 347–368, 2002. View at Zentralblatt MATH · View at Scopus
  17. G. T. Whyburn, Topological Analysis, Princeton Mathematical Series. No. 23, Princeton University Press, Princeton, NJ, USA, 1958.
  18. G. W. Zhang and J. X. Sun, “Positive solutions of m-point boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 291, no. 2, pp. 406–418, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. M. A. Krasnoselskii, Positive Solutions of Operator Equations, P. Noordhoff Limited, Groningen, The Netherlands, 1964.
  20. D. J. Guo and J. X. Sun, Nonlinear Integral Equations, Shandong Science and Technology Press, Jinan, China, 1987.
  21. Y. J. Liu and W. G. Ge, “Positive solutions of two-point boundary value problems for 2n-order differential equations dependent on all derivatives,” Applied Mathematics Letters, vol. 18, no. 2, pp. 209–218, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. P. H. Rabinowitz, “Some global results for nonlinear eigenvalue problems,” Journal of Functional Analysis, vol. 7, no. 3, pp. 487–513, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus