Volume 37 • Number 1 • 2014   • Multiple Solutions of Nonlinear Boundary Value Problems for Fractional Differential Equations Zhenhai Liu and Jitai Liang Abstract. In this paper, we study nonlinear boundary value problems of fractional differential equations. \begin{equation}\label{equ1} %\left\{\begin{array}{lll}\mathbf{D}_{0^{+}}^{q}x(t)=f(t,x(t))~~~~~t\in %J=[0,T]\\ %g( x(0),x(T), x(\eta))=0~~~~~~~~~ \eta\in [0,T],\end{array}\right. \begin{cases}%{lll} \mathbf{D}_{0^{+}}^{q}x(t)=f(t,x(t)) & t\in J=[0,T]\\ g\big(x(0),x(T), x(\eta)\big)=0 & \eta\in [0,T], \end{cases} \end{equation} where $\mathbf{D}_{0^{+}}$ denotes the Caputo fractional derivative, $0<q\leq 1$. Some new results on the multiple solutions are obtained by the use of the Amann theorem and the method of upper and lower solutions. An example is also given to illustrate our results. 2010 Mathematics Subject Classification: 26A33, 34K37 Full text: PDF