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 and Applications

Volumn 72, Issue 2, 2009, Pages 710-719

  Jiang, Daqing ^a   Yuan, Chengjun ^a,b  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b HARBIN UNIVERSITY   (China)

Author keywords

34B18; Boundary value problem; Fixed point theorem in cones; Positive solution; Riemann Liouville's fractional derivative

Indexed keywords

DIRICHLET; FIXED POINT THEOREM IN CONES; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; GREEN FUNCTION; POSITIVE SOLUTION;

BOUNDARY VALUE PROBLEMS; GREEN'S FUNCTION; ORDINARY DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 71649090846     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.07.012     Document Type: Article

References (18)

1. Agrawal O.P. Formulation of Euler-Lagrange equations for fractional variational problems. J. Math. Anal. Appl. 272 (2002) 368-379
2. Delbosco D., and Rodino L. Existence and uniqueness for a nonlinear fractional differential equation. J. Math. Appl. 204 (1996) 609-625
3. Leggett R.W., and Williams L.R. Multiple positive solutions of nonlinear operators on ordered Banach spaces. Indiana Univ. Math. J. 28 (1979) 673-688
4. Podlubny I. Fractional Differential Equations. Mathematics in Science and Engineering vol. 198 (1999), Academic Press, New Tork, London, Toronto
5. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integral And Derivatives (Theory and Applications) (1993), Gordon and Breach, Switzerland
6. Bai Z., and Lü H. Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311 (2005) 495-505
7. Zhang S.-q. The existence of a positive solution for a nonlinear fractional differential equation. J. Math. Anal. Appl. 252 (2000) 804-812
8. Zhang S.-q. Existence of positive solution for some class of nonlinear fractional differential equations. J. Math. Anal. Appl. 278 1 (2003) 136-148
9. Wei Z. Positive solution of singular Dirichlet boundary value problems for second order differential equation system. J. Math. Anal. Appl. 328 (2007) 1255-1267
10. Zhang X., Liu L., and Wu Y. Positive solutions of nonresonance semipositone singular Dirichlet boundary value problems. Nonlinear Anal. TMA 68 1 (2008) 97-108
11. Agarwal R.P., and O'Regan D. Twin solutions to singular Dirichlet problems. J. Math. Anal. Appl. 240 2 (1999) 433-445
12. Tersenov A.S., and Tersenov A.S. The problem of Dirichlet for evolution one-dimensional p-Laplacian with nonlinear source. J. Math. Anal. Appl. 340 (2008) 1109-1119
13. Lin X., and Jiang D. Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations. J. Math. Anal. Appl. 321 2 (2006) 501-514
14. O'Regan D. Singular Dirichlet boundary value problems. Superlinear and nonresonant case. Nonlinear Anal. 29 2 (1997) 221-245
15. Krasnosel'skii M.A. Positive Solutions of Operator Equations (1964), Noordhoff Gronigen, Netherland
16. Lakshmikantham V., and Vatsala A.S. Theory of fractional differential inequalities and applications. Commun. Appl. Anal. 11 3-4 (2007) 395-402
17. Lakshmikantham V., and Vatsala A.S. General uniqueness and monotone iterative technique for fractional differential equations. Appl. Math. Lett. 21 (2008) 828-834
18. Lakshmikantham V., and Vatsala A.S. Basic theory of fractional differential equations. Nonlinear Anal. TMA 69 8 (2008) 2677-2682