Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 513051, 7 pages
http://dx.doi.org/10.1155/2014/513051
Research Article

Existence and Nonexistence of Positive Solutions for a Higher-Order Three-Point Boundary Value Problem

1College of Electron and Information, Zhejiang University of Media and Communications, Hangzhou, Zhejiang 310018, China
2Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia

Received 3 November 2013; Accepted 27 December 2013; Published 12 January 2014

Academic Editor: Simeon Reich

Copyright © 2014 Yongping Sun 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. R. P. Agarwal, D. O'Regan, and V. Lakshmikantham, “Singular p,np focal and n,p higher order boundary value problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 42, no. 2, pp. 215–228, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. V. Baxley and C. R. Houmand, “Nonlinear higher order boundary value problems with multiple positive solutions,” Journal of Mathematical Analysis and Applications, vol. 286, no. 2, pp. 682–691, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. B. Yang, “Positive solutions for the n,p boundary value problem,” Electronic Journal of Qualitative Theory of Differential Equations, no. 31, pp. 1–13, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. P. W. Eloe and B. Ahmad, “Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions,” Applied Mathematics Letters, vol. 18, no. 5, pp. 521–527, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. R. Graef and T. Moussaoui, “A class of nth-order BVPs with nonlocal conditions,” Computers & Mathematics with Applications, vol. 58, no. 8, pp. 1662–1671, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. 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
  7. J. R. Graef, J. Henderson, and B. Yang, “Positive solutions of a nonlinear higher order boundary-value problem,” Electronic Journal of Differential Equations, vol. 2007, no. 45, pp. 1–10, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. R. Graef, J. Henderson, P. J. Y. Wong, and B. Yang, “Three solutions of an nth order three-point focal type boundary value problem,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 10, pp. 3386–3404, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. X. Zhang, M. Feng, and W. Ge, “Existence and nonexistence of positive solutions for a class of nth-order three-point boundary value problems in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 2, pp. 584–597, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Z. Du, W. Liu, and X. Lin, “Multiple solutions to a three-point boundary value problem for higher-order ordinary differential equations,” Journal of Mathematical Analysis and Applications, vol. 335, no. 2, pp. 1207–1218, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Y. Gao, “Existence and uniqueness of solutions for nth-order nonlinear three-point boundary value problems,” Dynamics of Continuous, Discrete & Impulsive Systems A, vol. 15, no. 2, pp. 243–250, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. R. Graef, C. Qian, and B. Yang, “A three point boundary value problem for nonlinear fourth order differential equations,” Journal of Mathematical Analysis and Applications, vol. 287, no. 1, pp. 217–233, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. R. Graef and B. Yang, “Positive solutions to a multi-point higher order boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 316, no. 2, pp. 409–421, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y. Ji and Y. Guo, “The existence of countably many positive solutions for nonlinear nth-order three-point boundary value problems,” Boundary Value Problems, vol. 2009, Article ID 572512, 18 pages, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. I. Y. Karaca, “Positive solutions of an nth order three-point boundary value problem,” The Rocky Mountain Journal of Mathematics, vol. 43, no. 1, pp. 205–224, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. X.-J. Liu, W.-H. Jiang, and Y.-P. Guo, “Multi-point boundary value problems for higher order differential equations,” Applied Mathematics E-Notes, vol. 4, pp. 106–113, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Y. Liu and W. Ge, “Positive solutions for n1,1 three-point boundary value problems with coefficient that changes sign,” Journal of Mathematical Analysis and Applications, vol. 282, no. 2, pp. 816–825, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. P. K. Palamides, “Multi point boundary-value problems at resonance for n-order differential equations: positive and monotone solutions,” Electronic Journal of Differential Equations, vol. 2004, no. 25, pp. 1–14, 2004. View at Google Scholar · View at MathSciNet
  19. X. Zhang, L. Liu, and H. Zou, “Positive solutions of fourth-order singular three point eigenvalue problems,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1359–1367, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. R. P. Agarwal, D. O'Regan, and P. J. Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic, Boston, Mass, USA, 1999. View at MathSciNet
  21. R. Avery, J. Henderson, and D. O'Regan, “Functional compression-expansion fixed point theorem,” Electronic Journal of Differential Equations, vol. 2008, no. 22, pp. 1–12, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. 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, San Diego, Calif, USA, 1988. View at MathSciNet