Positive solutions for nonlinear fractional semipositone differential equation with nonlocal boundary conditions
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Authors
Xinan Hao
- School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, P. R. China.
Lishan Liu
- School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, P. R. China.
- Department of Mathematics and Statistics, Curtin University, Perth, 6845WA, Australia.
Yonghong Wu
- Department of Mathematics and Statistics, Curtin University, Perth, 6845WA, Australia.
Abstract
In this paper, we study the existence of positive solutions to the nonlinear fractional order singular and
semipositone nonlocal boundary value problem
\[
\begin{cases}
\mathfrak{D}^\alpha_{0^+}u(t)+f(t,u(t))=0,\,\,\,\,\, 0<t<1,\\
u(0)=u'(0)=...=u^{(n-2)}(0)=0,\,\,\,\,\, u(1)=\mu\int^1_0 u(s)ds.
\end{cases}
\]
by using the Leray-Schauder nonlinear alternative and a fixed-point theorem on cones, where \(0 < \mu <
\alpha; 2 \leq n - 1 < \alpha \leq n, \mathfrak{D}^\alpha_{0^+}\)
is the standard Riemann-Liouville derivative, and f(t; u) is semipositone and
may be singular at u = 0.
Share and Cite
ISRP Style
Xinan Hao, Lishan Liu, Yonghong Wu, Positive solutions for nonlinear fractional semipositone differential equation with nonlocal boundary conditions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 3992--4002
AMA Style
Hao Xinan, Liu Lishan, Wu Yonghong, Positive solutions for nonlinear fractional semipositone differential equation with nonlocal boundary conditions. J. Nonlinear Sci. Appl. (2016); 9(6):3992--4002
Chicago/Turabian Style
Hao, Xinan, Liu, Lishan, Wu, Yonghong. "Positive solutions for nonlinear fractional semipositone differential equation with nonlocal boundary conditions." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 3992--4002
Keywords
- Singular fractional differential equation
- semipositone
- positive solutions
- nonlocal boundary conditions.
MSC
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