Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation
Moustafa El-Shahed
Source: Abstr. Appl. Anal. Volume 2007 (2007), 8 pages.
Abstract
We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: $D_{0+}^{\alpha} u(t) + \lambda a(t) f(u(t)) =0$ $0\lt t \lt 1$ $u(0) = u^\prime (0) = u^\prime (1) = 0$ where $2\lt \alpah \lt 3$ is a real number and $D_{0+}^{\alpha }$ is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.
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Permanent link to this document: http://projecteuclid.org/euclid.aaa/1204126601
Digital Object Identifier: doi:10.1155/2007/10368
Abstract and Applied Analysis