Positive solutions for three-point nonlinear fractional boundary value problems.
Saadi, A., Benbachir, M. (2011)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Saadi, A., Benbachir, M. (2011)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Wang, Jinhua, Xiang, Hongjun, Liu, Zhigang (2010)
International Journal of Differential Equations
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Tian, Yuansheng, Chen, Anping (2009)
Abstract and Applied Analysis
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Svatoslav Staněk (2013)
Open Mathematics
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We investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their...
Bai, Chuanzhi (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Chen, Anping, Chen, Yi (2011)
Boundary Value Problems [electronic only]
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Yuan, Chengjun, Jiang, Daqing, Xu, Xiaojie (2009)
Mathematical Problems in Engineering
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Lv, Zhi-Wei (2011)
Advances in Difference Equations [electronic only]
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Liang, Jin, Lv, Zhi-Wei (2011)
Advances in Difference Equations [electronic only]
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Berroug, Tarik (2010)
Applied Mathematics E-Notes [electronic only]
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Svatoslav Staněk (1995)
Annales Polonici Mathematici
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The differential equation of the form , a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.