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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 578672, 10 pages
http://dx.doi.org/10.1155/2014/578672
Research Article

The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions

1School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China
2College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China

Received 10 March 2014; Accepted 13 May 2014; Published 17 July 2014

Academic Editor: Abdul Latif

Copyright © 2014 Yanping Guo 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. J. Wang, C. Yu, and Y. Guo, “Triple positive solutions of a nonlocal boundary value problem for singular differential equations with p-Laplacian,” Abstract and Applied Analysis, vol. 2013, Article ID 613672, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. Feng, “Existence of symmetric positive solutions for a boundary value problem with integral boundary conditions,” Applied Mathematics Letters, vol. 24, no. 8, pp. 1419–1427, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. 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, 20 pages, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. 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 and Applications, vol. 73, no. 6, pp. 1653–1662, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. 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 MathSciNet · View at Scopus
  6. 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 MathSciNet · View at Scopus
  7. A. Cabada and R. R. Enguica, “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 MathSciNet · View at Scopus
  8. 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 Google Scholar · View at MathSciNet
  9. 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, pp. 1–17, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. 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 MathSciNet · View at Scopus
  11. 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 A: Mathematics, vol. 138, no. 2, pp. 427–446, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. B. Zhang, L. Kong, Y. Sun, and X. Deng, “Existence of positive solutions for {BVP}s of fourth-order difference equations,” Applied Mathematics and Computation, vol. 131, no. 2-3, pp. 583–591, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. L. Kong, Q. Kong, and B. Zhang, “Positive solutions of boundary value problems for third-order functional difference equations,” Computers & Mathematics with Applications, vol. 44, no. 3-4, pp. 481–489, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. 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 and Applications, vol. 69, no. 10, pp. 3310–3321, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Y. Guo, F. Yang, and Y. Liang, “Positive solutions for nonlocal fourth-order boundary value problems with all order derivatives,” Boundary Value Problems, vol. 2012, article 29, 12 pages, 2012. View at Google Scholar · View at MathSciNet
  16. Q. Wang, Y. Guo, and Y. Ji, “Positive solutions for fourth-order nonlinear differential equation with integral boundary conditions,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 684962, 10 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. X. Zhang and W. Ge, “Symmetric positive solutions of boundary value problems with integral boundary conditions,” Applied Mathematics and Computation, vol. 219, no. 8, pp. 3553–3564, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5 of Notes and Reports in Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1988. View at MathSciNet