Existence of Multiple Positive Solutions for p-Laplacian Fractional Order Boundary Value Problems

Article Sidebar

PDF
Cite as:
K. R. Prasad, B. M. B. Krushna, Existence of Multiple Positive Solutions for p-Laplacian Fractional Order Boundary Value Problems, Int. J. Anal. Appl., 6 (1) (2014), 63-81.

Main Article Content

K. R. Prasad, B. M. B. Krushna

Abstract

This paper deals with the existence of at least one and multiple positive solutions for p-Laplacian fractional order two-point boundary value problems, by applying Krasnosel'skii and five functionals fixed point theorems.

Article Details

References

  1. R. P. Agarwal, D. O'Regan and P. J. Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
  2. D. R. Anderson and J. M. Davis, Multiple positive solutions and eigenvalues for third order right focal boundary value problems, J. Math. Anal. Appl., 267(2002), 135-157.
  3. R. I. Avery, A generalization of the Leggett-Williams fixed point theorem, Math. Sci. Res. Hot-line, 3(1999), 9-14.
  4. R. I. Avery, J. Henderson, Existence of three positive pseudo-symmetric solutions for a onedimensional p-Laplacian, J. Math. Anal. Appl., 277(2003), 395-404.
  5. C. Bai, Existence of positive solutions for boundary value problems of fractional functional differential equations, Electronic Journal of Qualitative Theory of Differential Equations, 30(2010), 1-14.
  6. Z. Bai and H. L ¨u, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311(2005), 495-505.
  7. G. Chai, Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator, Boundary Value Problems, 2012(2012), 1-18.
  8. T. Chen and W. Liu, An anti-periodic boundary value problem for the fractional differential equation with a p-Laplacian operator, Appl. Math. Lett., 25(2012), 1671-1675.
  9. J. M. Davis, J. Henderson, K. R. Prasad and W. Yin, Eigenvalue intervals for non-linear right focal problems, Appl. Anal., 74(2000), 215-231.
  10. R. Dehghani and K. Ghanbari, Triple positive solutions for boundary value problem of a nonlinear fractional differential equation, Bulletin of the Iranian Mathematical Society, 33(2007), 1-14.
  11. L. H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc., 120(1994), 743-748.
  12. D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Acadamic Press, San Diego, 1988.
  13. A. A. Kilbas, H. M. Srivasthava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Vol. 204, Elsevier Science, Amsterdam, 2006.
  14. L. Kong and J. Wang, Multiple positive solutions for the one-dimensional p-Laplacian, Nonlinear Analysis, 42(2000), 1327-1333.
  15. M. A. Krasnosel'skii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.
  16. R. W. Leggett and L. R. Williams, Multiple positive fixed points of nonlinear operator on order Banach spaces, Indiana Univer. Math. J., 28(1979), 673-688.
  17. D. O'Regan, Some general existence principles and results for (φ(y 0 ))0 = qf(t, y, y0 ), 0 < t < 1, SIAM J. Math. Appl., 24(1993), 648-668.
  18. I. Podulbny, Fractional Diffrential Equations, Academic Press, San Diego, 1999.
  19. K. R. Prasad and P. Murali, Eigenvalue intervals of two-point boundary value problems for general n th order differential equations, Nonlinear Studies, Vol. 18, No.2(2011), 167-176.
  20. K. R. Prasad and B. M. B. Krushna, Multiple positive solutions for a coupled system of Riemann-Liouville fractional order two-point boundary value problems, Nonlinear Studies, Vol.20, No.4(2013), 501-511.
  21. K. R. Prasad, B. M. B. Krushna and N. Sreedhar, Eigenvalues for iterative systems of (n, p)- type fractional order boundary value problems, International Journal of Analysis and Applications, Vol. 5, No. 2(2014), 136-146.
  22. K. R. Prasad and B. M. B. Krushna, Eigenvalues for iterative systems of Sturm-Liouville fractional order two-point boundary value problems, Fract. Calc. Appl. Anal., Vol. 17, No.3(2014), 638-653, DOI: 10.2478/s13540-014-0190-4.
  23. C. Yang and J. Yan, Positive solutions for third-order Sturm-Liouville boundary value problems with p-Laplacian, Comput. Math. Appl., 59(2010), 2059-2066.