  This work is devoted to study the existence of infinitely many weak solutions
to nonlocal equations involving a general integrodifferential operator of
fractional type. These equations have a variational structure and we find a
sequence of nontrivial weak solutions for them exploiting the
${\mathbb{Z}}_2$-symmetric version of the Mountain Pass Theorem. To make the
nonlinear methods work, some careful analysis of the fractional spaces involved
is necessary. As a particular case, we derive an existence theorem for the
fractional Laplacian, finding nontrivial solutions of the equation $$
\left\{\begin{array}{ll} (-\Delta)^s u=f(x,u) & {\mbox{in}} \Omega\\ u=0 &
{\mbox{in}} \erre^n\setminus \Omega. \end{array} \right. $$ As far as we know,
all these results are new and represent a fractional version of classical
theorems obtained working with Laplacian equations.
