  Motivated by mechanical problems where external forces are non-smooth, we
consider the differential inclusion problem \[ \begin{cases}
  -\Delta u(x)\in \partial F(u(x))+\lambda \partial G(u(x))\ \mbox{in}\ \Omega
\newline
  u\geq 0\ \mbox{in}\ \Omega \newline
  u= 0\ \mbox{on}\ \partial\Omega,
  \end{cases} \ \ \ \ \ \ \ \ \ \ \ \ {({\mathcal D}_\lambda)}
  \] where $\Omega \subset {\mathbb R}^n$ is a bounded open domain, and
$\partial F$ and $\partial G$ stand for the generalized gradients of the
locally Lipschitz functions $F$ and $G$. In this paper we provide a quite
complete picture on the number of solutions of $({\mathcal D}_\lambda)$
whenever $\partial F$ oscillates near the origin/infinity and $\partial G$ is a
generic perturbation of order $p>0$ at the origin/infinity, respectively. Our
results extend in several aspects those of Krist\'aly and Moro\c{s}anu [J.
Math. Pures Appl., 2010].
