Table of Contents Author Guidelines Submit a Manuscript
International Journal of Differential Equations
Volume 2016, Article ID 6906049, 10 pages
http://dx.doi.org/10.1155/2016/6906049
Research Article

Multiplicity of Positive Solutions for Fractional Differential Equation with -Laplacian Boundary Value Problems

Department of Mathematics, Jazan University, P.O. Box 114, Jazan, Saudi Arabia

Received 15 October 2015; Accepted 6 April 2016

Academic Editor: Kanishka Perera

Copyright © 2016 Sabbavarapu Nageswara Rao. 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 P. J. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic, Dordrecht, The Netherlands, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  2. D. R. Anderson and J. M. Davis, “Multiple solutions and eigenvalues for third-order right focal boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 267, no. 1, pp. 135–157, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. R. W. Leggett and L. R. Williams, “Multiple positive fixed points of nonlinear operators on ordered Banach spaces,” Indiana University Mathematics Journal, vol. 28, no. 4, pp. 673–688, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y. Sun, Q. Sun, and X. Zhang, “Existence and nonexistence of positive solutions for a higher-order three-point boundary value problem,” Abstract and Applied Analysis, vol. 2014, Article ID 513051, 7 pages, 2014. View at Publisher · View at Google Scholar
  5. S. Nageswararao, “Solvability of second order delta-nabla p-Laplacian m-point eigenvalue problem on time scales,” TWMS Journal of Applied and Engineering Mathematics, vol. 5, no. 1, pp. 98–109, 2015. View at Google Scholar
  6. M. Ramaswamy and R. Shivaji, “Multiple positive solutions for classes of p-Laplacian equations,” Differential and Integral Equations, vol. 17, no. 11-12, pp. 1255–1261, 2004. View at Google Scholar · View at MathSciNet
  7. C. Yang and J. Yan, “Positive solutions for third-order Sturm-Liouville boundary value problems with p-Laplacian,” Computers & Mathematics with Applications, vol. 59, no. 6, pp. 2059–2066, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. C. Zhai and C. Guo, “Positive solutions for third-order Sturm-Liouville boundary-value problems with p-Laplacian,” Electronic Journal of Differential Equations, vol. 2009, no. 154, pp. 1–9, 2009. View at Google Scholar
  9. S. Liang and J. Zhang, “Positive solutions for boundary value problems of nonlinear fractional differential equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 11, pp. 5545–5550, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. S. Nageswararao, “Multiple positive solutions for a system of Riemann-Liouville fractional order two-point boundary value problems,” Panamerican Mathematical Journal, vol. 25, no. 1, pp. 66–81, 2015. View at Google Scholar
  11. S. Nageswararao, “Existence and multiplicity for a system of fractional higher-order two-pointboundary value problem,” Journal of Applied Mathematics and Computing, vol. 53, pp. 93–107, 2016. View at Publisher · View at Google Scholar
  12. Y. Zhao, S. Sun, Z. Han, and M. Zhang, “Positive solutions for boundary value problems of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 217, no. 16, pp. 6950–6958, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. G. Chai, “Positive solutions for boundary value problem of fractional Differential equation with p-Laplacian operator,” Boundary Value Problems, vol. 2012, article 18, 2012. View at Google Scholar
  14. Z. Han, H. Lu, S. Sun, and D. Yang, “Positive solutions to boundary-value problems of p-Laplacian fractional differential equations with a parameter in the boundary conditions,” Electronic Journal of Differential Equations, vol. 2012, no. 213, pp. 1–14, 2012. View at Google Scholar
  15. H. Lu, Z. Han, and S. Sun, “Multiplicity of positive solutions for Sturm-Liouville boundary value problems of fractional differential equations with p-Laplacian,” Boundary Value Problems, vol. 2014, article 26, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. C. T. Ledesma, “Boundary value problem with fractional p-Laplacian operator,” Advances in Nonlinear Analysis, 2015. View at Publisher · View at Google Scholar
  17. Y. Li and A. Qi, “Positive solutions for multi-point boundary value problems of fractional differential equations with p-Laplacian,” Mathematical Methods in the Applied Sciences, vol. 39, no. 6, pp. 1425–1434, 2016. View at Publisher · View at Google Scholar
  18. K. R. Prasad and B. M. B. Krushna, “Existence of multiple positive solutions for p-Laplacian fractional order boundary value problems,” International Journal of Analysis and Applications, vol. 6, no. 1, pp. 63–81, 2014. View at Google Scholar
  19. B. Zhang, “Solvability of fractional boundary value problems with p-Laplacian operator,” Advances in Difference Equations, vol. 2015, article 352, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  20. A. Kameswararao and S. Nageswararao, “Eigenvalue problems for systems of nonlinear higher order boundary value problems,” Journal of Applied Mathematics and Informatics, vol. 28, no. 3-4, pp. 711–721, 2010. View at Google Scholar
  21. D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Orlando, Fla, USA, 1988. View at MathSciNet
  22. K. Deimling, Nonlinear Functional Analysis, Springer, New York, NY, USA, 1985. View at Publisher · View at Google Scholar · View at MathSciNet