Existence of unbounded positive solutions for BVPs of singular fractional differential equations


Authors

Yuji Liu - Department of Mathematics, Guangdong University of Business Studies, Guangzhou 510320, P. R. China. Haiping Shi - Basic Courses Department, Guangdong Construction Vocational Technology Institute, Guangzhou 510450, P. R. China.


Abstract

In this article, we establish the existence of multiple unbounded positive solutions to the boundary value problem of the nonlinear singular fractional differential equation \[ \begin{cases} D^\alpha_{ 0^+}u(t) + f(t; u(t)) = 0; t \in (0; 1); 1 < \alpha < 2,\\ [I^{2-\alpha}_{ 0^+} u(t)]'|_{t=0} = 0\\ u(1) = 0. \end{cases} \] Our analysis relies on the well known fixed point theorems in the cones in Banach spaces. Here \(f\) is singular at \(t = 0\) and \(t = 1\).


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ISRP Style

Yuji Liu, Haiping Shi, Existence of unbounded positive solutions for BVPs of singular fractional differential equations, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 4, 281--293

AMA Style

Liu Yuji, Shi Haiping, Existence of unbounded positive solutions for BVPs of singular fractional differential equations. J. Nonlinear Sci. Appl. (2012); 5(4):281--293

Chicago/Turabian Style

Liu, Yuji, Shi, Haiping. "Existence of unbounded positive solutions for BVPs of singular fractional differential equations." Journal of Nonlinear Sciences and Applications, 5, no. 4 (2012): 281--293


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