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.