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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 162418, 7 pages
http://dx.doi.org/10.1155/2013/162418
Research Article

Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations

School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China

Received 3 April 2013; Accepted 30 September 2013

Academic Editor: Soheil Salahshour

Copyright © 2013 Yansheng Liu. 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. B. Ahmad and J. J. Nieto, “Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations,” Abstract and Applied Analysis, vol. 2009, Article ID 494720, 9 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  2. K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, vol. 2004, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  3. A. A. Kilbas and J. J. Trujillo, “Differential equations of fractional order: methods, results and problems—I,” Applicable Analysis, vol. 78, no. 1-2, pp. 153–192, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. A. Kilbas and J. J. Trujillo, “Differential equations of fractional order: methods, results and problems—II,” Applicable Analysis, vol. 81, no. 2, pp. 435–493, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  5. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  6. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integral and Derivatives (Theory and Applications), Gordon and Breach, Yverdon, Switzerland, 1993. View at MathSciNet
  7. Z. Wei, Q. Li, and J. Che, “Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative,” Journal of Mathematical Analysis and Applications, vol. 367, no. 1, pp. 260–272, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  8. C. Tian and Y. Liu, “Multiple positive solutions for a class of fractional singular boundary value problems,” Georgian Academy of Sciences, vol. 56, pp. 115–131, 2012. View at MathSciNet
  9. 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 MathSciNet
  10. D. Jiang and C. Yuan, “The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 2, pp. 710–719, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  11. Y. Liu and D. O'Regan, “Bifurcation techniques for Lidstone boundary value problems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 9, pp. 2801–2812, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  12. R. Ma and J. Xu, “Bifurcation from interval and positive solutions of a nonlinear fourth-order boundary value problem,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 1, pp. 113–122, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Xu and R. Ma, “Bifurcation from interval and positive solutions for second order periodic boundary value problems,” Applied Mathematics and Computation, vol. 216, no. 8, pp. 2463–2471, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  14. Y. Liu and H. Yu, “Bifurcation of positive solutions for a class of boundary value problems of fractional differential inclusions,” Abstract and Applied Analysis, vol. 2013, Article ID 942831, 8 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. K. Schmitt and R. C. Thompson, Nonlinear Analysis and Differential Equations: An Introduction, University of Utah Lecture Note, Salt Lake City, Utah, USA, 2004.
  16. K. Schmitt, “Positive solutions of semilinear elliptic boundary value problems,” in Topological Methods in Differential Equations and Inclusions, vol. 472, pp. 447–500, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995. View at MathSciNet
  17. D. Guo, Nonlinear Functional Analysis, Shandong Science and Technology Press, Jinan, China, 2001, (Chinese).