Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2010, Article ID 495138, 17 pages
http://dx.doi.org/10.1155/2010/495138
Research Article

Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with -Laplacian Operator

Department of Mathematics, Xiangnan University, Chenzhou 423000, China

Received 27 July 2009; Accepted 9 March 2010

Academic Editor: Rodica Costin

Copyright © 2010 Jinhua 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. H. Su, Z. Wei, and B. H. Wang, “The existence of positive solutions for a nonlinear four-point singular boundary value problem with a p-Laplacian operator,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 10, pp. 2204–2217, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. L. Yang, X. P. Liu, and M. Jia, “Multiplicity results for second-order m-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 324, no. 1, pp. 532–542, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. X. G. Zhang and L. S. Liu, “Positive solutions of fourth-order four-point boundary value problems with p-Laplacian operator,” Journal of Mathematical Analysis and Applications, vol. 336, no. 2, pp. 1414–1423, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y. P. Sun, “Optimal existence criteria for symmetric positive solutions to a three-point boundary value problem,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 5, pp. 1051–1063, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Z. B. Bai and W. G. Ge, “Existence of three positive solutions for some second-order boundary value problems,” Computers & Mathematics with Applications, vol. 48, no. 5-6, pp. 699–707, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D. Delbosco and L. Rodino, “Existence and uniqueness for a nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 204, no. 2, pp. 609–625, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. H. Jafari and V. D. Gejji, “Positive solutions of nonlinear fractional boundary value problems using adomian decomposition method,” Applied Mathematics and Computation, vol. 180, no. 2, pp. 700–706, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. H. Wang, H. J. Xiang, and Z. G. Liu, “Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations,” International Journal of Differential Equations, vol. 2010, Article ID 186928, 12 pages, 2010. View at Publisher · View at Google Scholar
  9. R. Dehghani and K. Ghanbari, “Triple positive solutions for boundary value problem of a nonlinear fractional differential equation,” Bulletin of the Iranian Mathematical Society, vol. 33, no. 2, pp. 1–14, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Q. Zhang, “Existence of solutions for a boundary value problem of fractional order,” Acta Mathematica Scientia, vol. 26, no. 2, pp. 220–228, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Q. Zhang, “Positive solutions for boundary value problems of nonlinear fractional differential equations,” Electronic Journal of Differential Equations, vol. 36, pp. 1–12, 2006. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. X. W. Su and L. L. Liu, “Existence of solution for boundary value problem of nonlinear fractional differential equation,” Applied Mathematics, vol. 22, no. 3, pp. 291–298, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Z. B. Bai and H. S. Lü, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Benchohra, S. Hamani, and S. K. Ntouyas, “Boundary value problems for differential equations with fractional order and nonlocal conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2391–2396, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  15. J. H. Wang, H. J. Xiang, and Z. G. Liu, “Positive solutions for three-point boundary values problems of nonlinear fractional differential equations with p-Laplacian,” Far East Journal of Applied Mathematics, vol. 37, pp. 33–47, 2009. View at Google Scholar
  16. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science, Yverdon, Switzerland, 1993. View at MathSciNet
  17. I. Podlubny, “Fractional Differential Equations,” vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet