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Erschienen in: Journal of Applied Mathematics and Computing 1-2/2017

22.02.2016 | Original Research

Bifurcation of positive solutions for a three-point boundary-value problem of nonlinear fractional differential equations

verfasst von: Xiangshan Kong, Haitao Li, Shulan Qin, Hongxin Zhao

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2017

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Abstract

This paper studies the bifurcation of positive solutions for a three-point boundary-value problem of nonlinear fractional differential equations with parameter. Using the topological degree theory and the bifurcation technique, the existence of positive solutions is investigated and some sufficient conditions are obtained. The study of two illustrative examples shows that the obtained new results are effective.

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Literatur
1.
Zurück zum Zitat Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)MATH Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)MATH
2.
Zurück zum Zitat Nonnenmacher, T.F., Metzler, R.: On the Riemann–Liouvile fractional calculus and some recent applications. Fractals 3, 557–566 (1995)MathSciNetCrossRefMATH Nonnenmacher, T.F., Metzler, R.: On the Riemann–Liouvile fractional calculus and some recent applications. Fractals 3, 557–566 (1995)MathSciNetCrossRefMATH
3.
Zurück zum Zitat Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives (Theory and Applications). Gordon and Breach, Basel (1993)MATH Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives (Theory and Applications). Gordon and Breach, Basel (1993)MATH
4.
Zurück zum Zitat Agarwal, R.P., Lupulescu, V., ORegan, D., Rahman, G.: Fractional calculus and fractional differential equations in nonreflexive Banach spaces. Commun. Nonlinear Sci. Numer. Simul. 20, 59–73 (2015)MathSciNetCrossRefMATH Agarwal, R.P., Lupulescu, V., ORegan, D., Rahman, G.: Fractional calculus and fractional differential equations in nonreflexive Banach spaces. Commun. Nonlinear Sci. Numer. Simul. 20, 59–73 (2015)MathSciNetCrossRefMATH
5.
Zurück zum Zitat Ahmad, B., Nieto, J.J.: Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Comput. Math. Appl. 58, 1838–1843 (2009)MathSciNetCrossRefMATH Ahmad, B., Nieto, J.J.: Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Comput. Math. Appl. 58, 1838–1843 (2009)MathSciNetCrossRefMATH
6.
Zurück zum Zitat Zhang, L., Ahmad, B., Wang, G., Agarwal, R.P.: Nonlinear fractional integro-differential equations on unbounded domains in a Banach space. J. Comput. Appl. Math. 249, 51–56 (2013)MathSciNetCrossRefMATH Zhang, L., Ahmad, B., Wang, G., Agarwal, R.P.: Nonlinear fractional integro-differential equations on unbounded domains in a Banach space. J. Comput. Appl. Math. 249, 51–56 (2013)MathSciNetCrossRefMATH
7.
Zurück zum Zitat Xu, X., Fei, X.: The positive properties of Green’s function for three point boundary-value problems of nonlinear fractional differential equations and its applications. Commun. Nonlinear Sci. Numer. Simul. 17, 1555–1565 (2012)MathSciNetCrossRefMATH Xu, X., Fei, X.: The positive properties of Green’s function for three point boundary-value problems of nonlinear fractional differential equations and its applications. Commun. Nonlinear Sci. Numer. Simul. 17, 1555–1565 (2012)MathSciNetCrossRefMATH
8.
Zurück zum Zitat Zhang, S.: Positive solutions for boundary-value problems of nonlinear fractional differential equations. Electron. J. Differ. Equ. 2006(36), 1–12 (2006)MathSciNetCrossRef Zhang, S.: Positive solutions for boundary-value problems of nonlinear fractional differential equations. Electron. J. Differ. Equ. 2006(36), 1–12 (2006)MathSciNetCrossRef
9.
Zurück zum Zitat Li, H., Kong, X., Yu, C.: Existence of three non-negative solutions for a three-point boundary-value problem of nonlinear fractional differential equations. Electron. J. Differ. Equ. 2012(88), 1–12 (2012)MathSciNetCrossRefMATH Li, H., Kong, X., Yu, C.: Existence of three non-negative solutions for a three-point boundary-value problem of nonlinear fractional differential equations. Electron. J. Differ. Equ. 2012(88), 1–12 (2012)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Zhao, Y., Sun, S., Han, Z., Zhang, M.: Positive solutions for boundary value problems of nonlinear fractional differential equations. Appl. Math. Comput. 217(16), 6950–6958 (2011)MathSciNetMATH Zhao, Y., Sun, S., Han, Z., Zhang, M.: Positive solutions for boundary value problems of nonlinear fractional differential equations. Appl. Math. Comput. 217(16), 6950–6958 (2011)MathSciNetMATH
11.
Zurück zum Zitat Zhao, Y., Sun, S., Han, Z., Li, Q.: The existence of multiple positive solutions for boundary-value problems of nonlinear fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 16, 2086–2097 (2011)MathSciNetCrossRefMATH Zhao, Y., Sun, S., Han, Z., Li, Q.: The existence of multiple positive solutions for boundary-value problems of nonlinear fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 16, 2086–2097 (2011)MathSciNetCrossRefMATH
12.
13.
Zurück zum Zitat Liang, S., Zhang, J.: Positive solutions for boundary value problems of nonlinear fractional differential equation. Nonlinear Anal. 2009(71), 5545–5550 (2009)MathSciNetCrossRefMATH Liang, S., Zhang, J.: Positive solutions for boundary value problems of nonlinear fractional differential equation. Nonlinear Anal. 2009(71), 5545–5550 (2009)MathSciNetCrossRefMATH
14.
Zurück zum Zitat Xu, X., Jiang, D., Hu, W., O’Regan, D., Agarwal, R.P.: Positive properties of Green’s function for three-point boundary-value problems of nonlinear fractional differential equations and its applications. Applicable Anal. 91(2), 323–343 (2012)MathSciNetCrossRefMATH Xu, X., Jiang, D., Hu, W., O’Regan, D., Agarwal, R.P.: Positive properties of Green’s function for three-point boundary-value problems of nonlinear fractional differential equations and its applications. Applicable Anal. 91(2), 323–343 (2012)MathSciNetCrossRefMATH
15.
16.
Zurück zum Zitat Ma, R.Y., Xu, J.: Bifurcation from interval and positive solutions of a nonlinear fourth order boundary value problem. Nonlinear Anal. 72, 113–122 (2010)MathSciNetCrossRefMATH Ma, R.Y., Xu, J.: Bifurcation from interval and positive solutions of a nonlinear fourth order boundary value problem. Nonlinear Anal. 72, 113–122 (2010)MathSciNetCrossRefMATH
17.
Zurück zum Zitat Xu, J., Ma, R.Y.: Bifurcation from interval and positive solutions for second order periodic boundary value problems. Appl. Math. Comput. 216, 2463–2471 (2010)MathSciNetMATH Xu, J., Ma, R.Y.: Bifurcation from interval and positive solutions for second order periodic boundary value problems. Appl. Math. Comput. 216, 2463–2471 (2010)MathSciNetMATH
18.
Zurück zum Zitat Liu, Y., Yu, H.: Bifurcation of positive solutions for a class of boundary value problems of fractional differential inclusions. Abstr. Appl. Anal., Article ID 942831 (2013) Liu, Y., Yu, H.: Bifurcation of positive solutions for a class of boundary value problems of fractional differential inclusions. Abstr. Appl. Anal., Article ID 942831 (2013)
19.
Zurück zum Zitat Schmitt, K., Thompson, R.C.: Nonlinear Analysis and Differential Equations: An Introduction. Lecture Note. University of Utah, Salt Lake City (2004) Schmitt, K., Thompson, R.C.: Nonlinear Analysis and Differential Equations: An Introduction. Lecture Note. University of Utah, Salt Lake City (2004)
20.
Zurück zum Zitat Schmitt, K.: Positive solutions of semilinear elliptic boundary value problem, pp. 447–500. Kluwer, Dordrecht (1995)MATH Schmitt, K.: Positive solutions of semilinear elliptic boundary value problem, pp. 447–500. Kluwer, Dordrecht (1995)MATH
21.
Zurück zum Zitat Guo, D.: Nonlinear Functional Analysis. Shandong Science and Technology Press, Jinan (2001) (in Chinese) Guo, D.: Nonlinear Functional Analysis. Shandong Science and Technology Press, Jinan (2001) (in Chinese)
Metadaten
Titel
Bifurcation of positive solutions for a three-point boundary-value problem of nonlinear fractional differential equations
verfasst von
Xiangshan Kong
Haitao Li
Shulan Qin
Hongxin Zhao
Publikationsdatum
22.02.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2017
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-016-0998-7

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