  In this paper we prove the existence of infinitely many nontrivial solutions
of the following equations driven by a nonlocal integro-differential operator
$L_K$ with concave-convex nonlinearities and homogeneous Dirichlet boundary
conditions \begin{eqnarray*}
  \mathcal{L}_{K} u + \mu\, |u|^{q-1}u + \lambda\,|u|^{p-1}u &=& 0
\quad\text{in}\quad \Omega, \\[2mm]
  u&=&0 \quad\mbox{in}\quad\mathbb{R}^N\setminus\Omega,
  \end{eqnarray*} where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$,
$N>2s$, $s\in(0, 1)$, $0<q<1<p\leq \frac{N+2s}{N-2s}$. Moreover, when $L_K$
reduces to the fractional laplacian operator $-(-\Delta)^s $,
$p=\frac{N+2s}{N-2s}$, $\frac{1}{2}(\frac{N+2s}{N-2s})<q<1$, $N>6s$,
$\lambda=1$, we find $\mu^*>0$ such that for any $\mu\in(0,\mu^*)$, there
exists at least one sign changing solution.
