  In this paper we establish the existence of two positive solutions for the
obstacle problem $$ \displaystyle \int_{\Re}\left[u'(v-u)'+(1+\lambda
V(x))u(v-u)\right] \geq \displaystyle \int_{\Re} f(u)(v-u), \forall v\in \Ka $$
where $f$ is a continuous function verifying some technical conditions and
$\Ka$ is the convex set given by $$ \Ka =\left\{v\in H^{1}(\Re); v \geq \varphi
\right\}, $$ with $\varphi \in H^{1}(\Re)$ having nontrivial positive part with
compact support in $\Re$.
  \vspace{0.2cm} \noindent \emph{2000 Mathematics Subject Classification} :
34B18, 35A15, 46E39.
  \noindent \emph{Key words}: Obstacle problem, Variational methods, Positive
solutions.
