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Erschienen in: Journal of Applied Mathematics and Computing 1-2/2013

01.07.2013 | Original Research

Positive solutions of m-point boundary value problems for a class of nonlinear fractional differential equations

verfasst von: Lin Wang, Xingqiu Zhang

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2013

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Abstract

This paper deals with the existence and multiplicity of positive solutions for a class of nonlinear fractional differential equations with m-point boundary value problems. We obtain some existence results of positive solution by using the properties of the Green’s function, u 0-bounded function and the fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator.

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Literatur
1.
Zurück zum Zitat Wang, Y.Q., Liu, L.S., Wu, Y.H.: Positive solutions for a nonlocal fractional differential equation. Nonlinear Anal. 74, 3599–3605 (2011) MathSciNetMATHCrossRef Wang, Y.Q., Liu, L.S., Wu, Y.H.: Positive solutions for a nonlocal fractional differential equation. Nonlinear Anal. 74, 3599–3605 (2011) MathSciNetMATHCrossRef
2.
3.
Zurück zum Zitat Xu, J.F., Wei, Z.L., Dong, W.: Uniqueness of positive solutions for a class of fractional boundary value problems. Appl. Math. Lett. 25, 590–593 (2012) MathSciNetMATHCrossRef Xu, J.F., Wei, Z.L., Dong, W.: Uniqueness of positive solutions for a class of fractional boundary value problems. Appl. Math. Lett. 25, 590–593 (2012) MathSciNetMATHCrossRef
4.
Zurück zum Zitat Xu, X.J., Jiang, D.Q., Yuan, C.J.: Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation. Nonlinear Anal. 71, 4676–4688 (2009) MathSciNetMATHCrossRef Xu, X.J., Jiang, D.Q., Yuan, C.J.: Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation. Nonlinear Anal. 71, 4676–4688 (2009) MathSciNetMATHCrossRef
5.
Zurück zum Zitat Jiang, D.Q., Yuan, C.J.: The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application. Nonlinear Anal. 72, 710–719 (2010) MathSciNetMATHCrossRef Jiang, D.Q., Yuan, C.J.: The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application. Nonlinear Anal. 72, 710–719 (2010) MathSciNetMATHCrossRef
6.
Zurück zum Zitat Zhao, X.K., Chai, C.W., Ge, W.G.: Positive solutions for fractional four-point boundary value problems. Commun. Nonlinear Sci. Numer. Simul. 16, 3665–3672 (2011) MathSciNetMATHCrossRef Zhao, X.K., Chai, C.W., Ge, W.G.: Positive solutions for fractional four-point boundary value problems. Commun. Nonlinear Sci. Numer. Simul. 16, 3665–3672 (2011) MathSciNetMATHCrossRef
7.
Zurück zum Zitat Bai, Z.B., Lü, H.S.: Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, 495–505 (2005) MathSciNetMATHCrossRef Bai, Z.B., Lü, H.S.: Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, 495–505 (2005) MathSciNetMATHCrossRef
8.
Zurück zum Zitat Li, C.F., Luo, X.N., Zhou, Y.: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. Comput. Math. Appl. 59, 1363–1375 (2010) MathSciNetMATHCrossRef Li, C.F., Luo, X.N., Zhou, Y.: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. Comput. Math. Appl. 59, 1363–1375 (2010) MathSciNetMATHCrossRef
9.
Zurück zum Zitat Wang, Y.Q., Liu, L.S.: Positive solutions for fractional m-point boundary value problem in Banach spaces. Acta Math. Sci. 32, 246–256 (2012) MATH Wang, Y.Q., Liu, L.S.: Positive solutions for fractional m-point boundary value problem in Banach spaces. Acta Math. Sci. 32, 246–256 (2012) MATH
10.
Zurück zum Zitat Bai, Z.B., Qiu, T.T.: Existence of positive solution for singular fractional differential equation. Appl. Math. Comput. 215, 2761–2767 (2009) MathSciNetMATHCrossRef Bai, Z.B., Qiu, T.T.: Existence of positive solution for singular fractional differential equation. Appl. Math. Comput. 215, 2761–2767 (2009) MathSciNetMATHCrossRef
11.
Zurück zum Zitat Goodrich, C.S.: Existence of a positive solution to a class of fractional differential equations. Appl. Math. Lett. 23, 1050–1055 (2010) MathSciNetMATHCrossRef Goodrich, C.S.: Existence of a positive solution to a class of fractional differential equations. Appl. Math. Lett. 23, 1050–1055 (2010) MathSciNetMATHCrossRef
12.
Zurück zum Zitat Xu, X.J., Jiang, D.Q., Yuan, C.J.: Multiple positive solutions to singular positone and semipositone Dirichlet-type boundary value problems of nonlinear fractional differential equations. Nonlinear Anal. 74, 5685–5696 (2011) MathSciNetMATHCrossRef Xu, X.J., Jiang, D.Q., Yuan, C.J.: Multiple positive solutions to singular positone and semipositone Dirichlet-type boundary value problems of nonlinear fractional differential equations. Nonlinear Anal. 74, 5685–5696 (2011) MathSciNetMATHCrossRef
13.
Zurück zum Zitat Cui, Y.J., Sun, J.X.: Positive solutions for second-order three-point boundary value problems in Banach spaces. Acta Math. Sci. 34, 743–751 (2011) MathSciNetMATH Cui, Y.J., Sun, J.X.: Positive solutions for second-order three-point boundary value problems in Banach spaces. Acta Math. Sci. 34, 743–751 (2011) MathSciNetMATH
14.
15.
Zurück zum Zitat Hao, X.A., Liu, L.S., Wu, Y.H., Sun, Q.: Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions. Nonlinear Anal. 73, 1653–1662 (2010) MathSciNetMATHCrossRef Hao, X.A., Liu, L.S., Wu, Y.H., Sun, Q.: Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions. Nonlinear Anal. 73, 1653–1662 (2010) MathSciNetMATHCrossRef
16.
17.
Zurück zum Zitat Guo, D.J., Sun, J.X.: Nonlinear Integral Equations. Shandong Science and Technology Press, Jinan (1987) Guo, D.J., Sun, J.X.: Nonlinear Integral Equations. Shandong Science and Technology Press, Jinan (1987)
18.
Zurück zum Zitat Krasnosel’skii, M.A.: Positive Solution of Operator Equation. Noordhoff, Groningen (1964) Krasnosel’skii, M.A.: Positive Solution of Operator Equation. Noordhoff, Groningen (1964)
19.
Zurück zum Zitat Guo, D.J., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, San Diego (1988) MATH Guo, D.J., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, San Diego (1988) MATH
Metadaten
Titel
Positive solutions of m-point boundary value problems for a class of nonlinear fractional differential equations
verfasst von
Lin Wang
Xingqiu Zhang
Publikationsdatum
01.07.2013
Verlag
Springer-Verlag
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2013
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-012-0626-0

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