Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 176, pp. 1-9.

Title: Existence of solutions for a  nonlinear fractional
       boundary value problem via a local minimum theorem

Author: Chuanzhi Bai (Huaiyin Normal Univ., China)

Abstract:
 This article concerns the existence of solutions to the  nonlinear
 fractional boundary-value problem
 $$\displaylines{
 \frac{d}{dt} \Big({}_0 D_t^{\alpha-1}({}_0^c D_t^{\alpha} u(t))
 -{}_t D_T^{\alpha-1}({}_t^c D_T^{\alpha} u(t))\Big)
 +\lambda f(u(t)) = 0, \quad\hbox{a.e. } t \in [0, T], \cr
 u(0) = u(T) = 0,
 }$$
 where $\alpha \in (1/2, 1]$,  and $\lambda$ is a positive real parameter.
 The approach is based on a local minimum theorem established by Bonanno.
 
Submitted July 30, 2012. Published October 12, 2012.
Math Subject Classifications: 58E05, 34B15, 26A33.
Key Words: Critical points; fractional differential equations;
           boundary-value problem.