Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem

Abstract

This paper is concerned with the existence of three solutions to a nonlinear fractional boundary value problem as follows: $(d/dt)((1/2){0}_{}{D}_{t}^{\alpha -1}{(}_{0}^{C}{D}_{t}^{\alpha }u(t))-(1/2){t}_{}{D}_{T}^{\alpha -1}{(}_{t}^{C}{D}_{T}^{\alpha }u(t)))+\lambda a(t)f(u(t))=0, \text{a}.\text{e}.\mathrm{ }t\in [0,T],$ $u(0)=u(T)=0,$ where $\alpha \in (1/2,1]$, and $\lambda $ is a positive real parameter. The approach is based on a critical-points theorem established by G. Bonanno.