Title: Existence of Positive Solutions for a Coupled System of (p, q)-Laplacian Fractional Higher Order Boundary Value Problems
Author(s): K.R. Prasad, B.M.B. Krushna, L.T. Wesen
Pages: 54-67
Cite as:
K.R. Prasad, B.M.B. Krushna, L.T. Wesen, Existence of Positive Solutions for a Coupled System of (p, q)-Laplacian Fractional Higher Order Boundary Value Problems, Int. J. Anal. Appl., 9 (1) (2015), 54-67.

Abstract


In this paper, we establish the existence of at least three positive solutions for a system of (p,q)-Laplacian fractional order two-point boundary value problems by applying five functionals fixed point theorem under suitable conditions on a cone in a Banach space.

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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. Google Scholar

  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. Google Scholar

  3. R. I. Avery, A generalization of the Leggett-Williams fixed point theorem, Math. Sci. Res. Hot-line, 3(1999), 9–14. Google Scholar

  4. R. I. Avery and J. Henderson, Existence of three positive pseudo-symmetric solutions for a onedimensional p-Laplacian, J. Math. Anal. Appl., 277(2003), 395–404. Google Scholar

  5. C. Bai, Existence of positive solutions for boundary value problems of fractional functional differential equations, Elec. J. Qual. Theory Diff. Equ., 30(2010), 1–14. Google Scholar

  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. Google Scholar

  7. G. Chai, Positive solutions for boundary value problem of fractional differential equation with pLaplacian operator, Bound. Value Probl., 2012(2012), 1–18. Google Scholar

  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. 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, 33(2007), 1–14. Google Scholar

  10. L. Diening, P. Lindqvist and B. Kawohl, Mini-Workshop: The p-Laplacian Operator and Applications, Oberwolfach Reports, 10(2013) 433–482. Google Scholar

  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. Google Scholar

  12. C. Goodrich, Existence of a positive solution to systems of differential equations of fractional order, Comput. Math. Appl., 62(2011), 1251–1268. Google Scholar

  13. D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Acadamic Press, San Diego, 1988. Google Scholar

  14. J. Henderson and S. K. Ntouyas, Positive solutions for systems of nonlinear boundary value problems, Nonlinear Stud., 15(2008), 51-60. Google Scholar

  15. 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. Google Scholar

  16. L. Kong and J. Wang, Multiple positive solutions for the one-dimensional p-Laplacian, Nonlinear Anal., 42(2000), 1327–1333. Google Scholar

  17. I. Podulbny, Fractional Diffrential Equations, Academic Press, San Diego, 1999. Google Scholar

  18. K. R. Prasad and B. M. B. Krushna, Multiple positive solutions for a coupled system of p-Laplacian fractional order two-point boundary value problems, Int. J. Differ. Equ., 2014(2014), Article ID 485647, 1–10. Google Scholar

  19. K. R. Prasad and B. M. B. Krushna, Multiple positive solutions for the system of (n, p)-type fractional order boundary value problems, Bull. Int. Math. Virtual Inst., 5(2015), 1–12. Google Scholar

  20. K. R. Prasad and B. M. B. Krushna, Solvability of p-Laplacian fractional higher order two-point boundary value problems, Commun. Appl. Anal., 19(2015), 659–678. Google Scholar

  21. X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett., 22(2009), 64–69. Google Scholar

  22. C. Yang, J. Yan, Positive solutions for third order Sturm–Liouville boundary value problems with p-Laplacian, Comput. Math. Appl., 59(2010), 2059–2066. Google Scholar