  The aim of this paper is to prove multiplicity of solutions for nonlocal
fractional equations modeled by $$ \left\{ \begin{array}{ll} (-\Delta)^s
u-\lambda u=f(x,u) & {\mbox{ in }} \Omega\\ u=0 & {\mbox{ in }}
\mathbb{R}^n\setminus \Omega\,, \end{array} \right. $$ where $s\in (0,1)$ is
fixed, $(-\Delta)^s$ is the fractional Laplace operator, $\lambda$ is a real
parameter, $\Omega\subset \mathbb{R}^n$, $n>2s$, is an open bounded set with
continuous boundary and nonlinearity $f$ satisfies natural superlinear and
subcritical growth assumptions. Precisely, along the paper we prove the
existence of at least three non-trivial solutions for this problem in a
suitable left neighborhood of any eigenvalue of $(-\Delta)^s$. At this purpose
we employ a variational theorem of mixed type (one of the so-called
$\nabla$-theorems).
