Positive solutions for a nonlocal fractional differential equation

Nonlinear Analysis, Theory, Methods and Applications

Volumn 74, Issue 11, 2011, Pages 3599-3605

  Wang, Yongqing ^a   Liu, Lishan ^a,b   Wu, Yonghong ^b  

^a QUFU NORMAL UNIVERSITY   (China)

^b CURTIN UNIVERSITY   (Australia)

Author keywords

Fixed point index; Fractional differential equation; Positive solution; Singular problem

Indexed keywords

FIXED-POINT INDEX; FIXED-POINT INDEX THEORY; FRACTIONAL DIFFERENTIAL EQUATIONS; NONLOCAL; POSITIVE SOLUTION; SIGNED MEASURE; SINGULAR BOUNDARY VALUE PROBLEMS; SINGULAR PROBLEM;

DIFFERENTIAL EQUATIONS;

EID: 79955563070     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2011.02.043     Document Type: Article

References (31)

1. I. Podlubny Fractional Differential Equations Mathematics in Science and Engineering vol. 198 1999 Academic Press New York, London, Toronto
2. A.A. Kilbas, H.M. Srivastava, and J.J. Nieto Theory and Applicational Differential Equations 2006 Elsevier Amsterdam
3. O.P. Agrawal Formulation of EulerLagrange equations for fractional variational problems J. Math. Anal. Appl. 272 2002 368 379
4. V. Lakshmikantham, and A.S. Vatsala General uniqueness and monotone iterative technique for fractional differential equations Appl. Math. Lett. 21 2008 828 834
5. T. Gnana Bhaskar, V. Lakshmikantham, and S. Leela Fractional differential equations with a KrasnoselskiiKrein type condition Nonlinear Anal. 3 2009 734 737
6. A. Arara, M. Benchohra, N Hamidi, and J.J. Nieto Fractional order differential equations on an unbounded domain Nonlinear Anal. 72 2010 580 586
7. Z. Bai On positive solutions of a nonlocal fractional boundary value problem Nonlinear Anal. 72 2010 916 924
8. 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 Anal. 72 2010 710 719
9. B. Ahmad, and A. Alsaedi Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integrodifferential equations of mixed type Nonlinear Anal. 3 2009 501 509
10. M. Benchohraa, S. Hamania, and S.K. Ntouyas Boundary value problems for differential equations with fractional order and nonlocal conditions Nonlinear Anal. 71 2009 2391 2396
11. M. El-Shahed, and J.J. Nieto Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order Comput. Math. Appl. 59 2010 3438 3443
12. B. Ahmad, and J.J. Nieto Existence results for higher order fractional differential inclusions with nonlocal boundary conditions Nonlinear Stud. 17 2010 131 138
13. H.A.H. Salem On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies Comput. Math. Appl. 224 2009 565 572
14. C.F. Li, X.N. Luo, and Y. Zhou Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations Comput. Math. Appl. 59 2010 1363 1375
15. R.P. Agarwal, D. O'Regan, and S. Stanek Positive solutions for Dirichlet problem of singular nonlinear fractional differential equations J. Math. Anal. Appl. 371 2010 57 68
16. C.S. Goodrich Existence of positive solution to a class of fractional differential equations Appl. Math. Lett. 23 2010 1050 1055
17. N. Kosmatov Integral equations and initial value problems for nonlinear differential equations of fractional order Nonlinear Anal. 70 2009 2521 2529
18. C. Yuan Multiple positive solutions for (n - 1, 1 )-type semipositone conjugate boundary value problems of nonlinear fractional differential equations Electron. J. Qual. Theory Differ. Equ. 36 2010 12 pp.
19. M. Feng, X. Zhang, and W. Ge New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions Bound. Value Probl. 2011 Art. ID 720702, 20 pp.
20. J. Allison, and N. Kosmatov Multi-point boundary value problems of fractional order Commun. Appl. Anal. 12 4 2008 451 458
21. R. Ma Existence of solutions of nonlinear m-point boundary value problems J. Math. Anal. Appl. 256 2001 556 567 (Pubitemid 33377587)
22. P.W. Eloe, and B. Ahmad Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions Appl. Math. Lett. 18 2005 521 527 (Pubitemid 40338074)
23. J.R.L. Webb, and K.Q. Lan Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type Topol. Methods Nonlinear Anal. 27 2006 91 116
24. J.R.L. Webb, and G. Infante Positive solutions of nonlocal boundary value problems: a unified approach J. London Math. Soc. 74 2006 673 693
25. J.R.L. Webb, and G. Infante Positive solutions of nonlocal boundary value problems involving integral conditions Nonlinear Differ. Equ. Appl. 15 2008 45 67
26. J.R.L. Webb Nonlocal conjugate type boundary value problems of higher order Nonlinear Anal. 71 2009 1933 1940
27. J.R.L. Webb, Higher order non-local (n - 1, 1 ) conjugate type boundary value problems, in: Mathematical Models in Engineering, Biology and Medicine, AIP Conf. Proc., in: Amer. Inst. Phys., vol. 1124, Melville, NY, 2009, pp. 332341.
28. J.R. Graef, and T. Moussaoui A class of nth-order BVPs with nonlocal conditions Comput. Math. Appl. 58 2009 1662 1671
29. X. Hao, L. Liu, Y. Wu, and Q. Sun Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions Nonlinear Anal. 73 2010 1653 1662
30. B. Yang Positive solutions of the (n - 1, 1 ) conjugate boundary value problem Electron. J. Qual. Theory Differ. Equ. 53 2010 13pp.
31. D. Guo, and V. Lakshmikantham Nonlinear Problems in Abstract Cones 1988 Academic Press New York