Electron. J. Diff. Equ., Vol. 2012 (2012), No. 176, pp. 1-9.

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

Chuanzhi Bai

This article concerns the existence of solutions to the nonlinear fractional boundary-value problem
 \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.

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Chuanzhi Bai
Department of Mathematics
Huaiyin Normal University
Huaian, Jiangsu 223300, China
email: czbai8@sohu.com

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