In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem(BVP) $-D_0^{alpha}+u(t)=lambda[f(t, u(t))+q(t)]$, 0 < t < 1 u(0) = u(1) = 0, where $lambda$ > 0 is a parameter, 1 < $alpha$ $leq$ 2, $D_{0+}^{alpha}$ is the standard Riemann-Liouville differentiation, f : [0, 1] ${ imes}{mathbb{R}}{ ightarrow}{mathbb{R}}$ is continuous, and q(t) : (0, 1) $ ightarrow$ [0, $+infty$] is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when $lambda$ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.