Liu, Xiping; Jia, Mei Multiple solutions for fractional differential equations with nonlinear boundary conditions. (English) Zbl 1193.34037 Comput. Math. Appl. 59, No. 8, 2880-2886 (2010). Summary: We study certain fractional differential equations with nonlinear boundary conditions. By means of the Amann theorem and the method of upper and lower solutions, some new results on the multiple solutions are obtained. Cited in 1 ReviewCited in 31 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34A08 Fractional ordinary differential equations 26A33 Fractional derivatives and integrals 45J05 Integro-ordinary differential equations Keywords:Caputo derivative; fractional differential equations; nonlinear boundary conditions; Amann theorem; method of upper and lower solutions; multiple solutions PDFBibTeX XMLCite \textit{X. Liu} and \textit{M. Jia}, Comput. Math. Appl. 59, No. 8, 2880--2886 (2010; Zbl 1193.34037) Full Text: DOI References: [1] El-Sayed, A. M.A., Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal., 33, 181-186 (1998) · Zbl 0934.34055 [2] Kilbas, A. A.; Trujillo, J. J., Differential equations of fractional order: Methods, results and problems I, Appl. Anal., 78, 153-192 (2001) · Zbl 1031.34002 [3] Kilbas, A. A.; Trujillo, J. J., Differential equations of fractional order: Methods, results and problems II, Appl. Anal., 81, 435-493 (2002) · Zbl 1033.34007 [4] Podlubny, I., (Fractional Differential Equations. Fractional Differential Equations, Mathematics in science and Engineering, vol. 198 (1999), Academic Press: Academic Press New York, London, Toronto) [5] Lakshmikantham, V.; Vatsalab, A. S., Basic theory of fractional differential equations, Nonlinear Anal., 69, 2677-2682 (2008) · Zbl 1161.34001 [6] Lakshmikantham, V., Theory of fractional functional differential equations, Nonlinear Anal., 69, 3337-3343 (2008) · Zbl 1162.34344 [7] Lakshmikantham, V.; Vatsalab, A. S., General uniqueness and monotone iterative technique for fractional differential equations, Appl. Math. Lett., 21, 828-834 (2008) · Zbl 1161.34031 [8] Bai, Z.; Lü, H., Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311, 495-505 (2005) · Zbl 1079.34048 [9] Xu, X.; Jiang, D.; Yuan, C., Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear Anal., 71, 4676-4688 (2009) · Zbl 1178.34006 [10] Amann, H., Fixed point equation and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18, 620-709 (1976) · Zbl 0345.47044 [11] Xu, X.; Sun, J., Solutions for an operator equation under the conditions of pairs of paralleled lower and upper solutions, Nonlinear Anal., 69, 2251-2266 (2008) · Zbl 1165.47044 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.