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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 605614, 9 pages
http://dx.doi.org/10.1155/2011/605614
Research Article

Existence Results for Singular Boundary Value Problem of Nonlinear Fractional Differential Equation

Department of Mathematics, Shandong University of Science and Technology, Qingdao 266510, China

Received 27 December 2010; Revised 2 March 2011; Accepted 3 March 2011

Academic Editor: Elena Braverman

Copyright © 2011 Yujun Cui. 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. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1993. View at Zentralblatt MATH
  3. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at Zentralblatt MATH
  4. S. Zhang, “Existence of solution 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 Zentralblatt MATH · View at MathSciNet
  5. Z. Bai and H. 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
  6. X. Xu, D. Jiang, and C. Yuan, “Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 10, pp. 4676–4688, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. A. Gatica, V. Oliker, and P. Waltman, “Singular nonlinear boundary value problems for second-order ordinary differential equations,” Journal of Differential Equations, vol. 79, no. 1, pp. 62–78, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Henderson and W. Yin, “Singular (k,nk) boundary value problems between conjugate and right focal,” Journal of Computational and Applied Mathematics, vol. 88, no. 1, pp. 57–69, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. P. W. Eloe and J. Henderson, “Singular nonlinear (k,nk) conjugate boundary value problems,” Journal of Differential Equations, vol. 133, no. 1, pp. 136–151, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. P. W. Eloe and J. Henderson, “Singular nonlinear multipoint conjugate boundary value problems,” Communications in Applied Analysis, vol. 2, no. 4, pp. 497–511, 1998. View at Zentralblatt MATH
  11. J. J. DaCunha, J. M. Davis, and P. K. Singh, “Existence results for singular three point boundary value problems on time scales,” Journal of Mathematical Analysis and Applications, vol. 295, no. 2, pp. 378–391, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. Feng and S. Liu, “Solvability of a third-order two-point boundary value problem,” Applied Mathematics Letters, vol. 18, no. 9, pp. 1034–1040, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Q. Yao and Y. Feng, “The existence of solution for a third-order two-point boundary value problem,” Applied Mathematics Letters, vol. 15, no. 2, pp. 227–232, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
  15. 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, Boston, Mass, USA, 1988.