  Let us consider the quasilinear problem
  \[ (P_\varepsilon) \ \ \left\{
  \begin{array}{ll}
  - \varepsilon^p \Delta _{p}u + u^{p-1} = f(u)
  & \hbox{in} \ \Omega
  \newline u>0 & \hbox{in} \ \Omega
  \newline u=0 & \hbox{on} \ \partial \Omega
  \end{array}
  \right.
  \]
  where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with smooth boundary,
$N\geq 2$, $1< p < 2$, $\varepsilon >0$ is a parameter and $f: \mathbb{R} \to
\mathbb{R}$ is a continuous function with $f(0)=0$, having a subcritical
growth. We prove that there exists $\varepsilon^* >0$ such that, for every
$\varepsilon \in (0, \varepsilon^*)$, $(P_\varepsilon)$ has at least
$2{\mathcal P}_1(\Omega)-1$ solutions, possibly counted with their
multiplicities, where ${\mathcal P}_t(\Omega)$ is the Poincar\'e polynomial of
$\Omega$. Using Morse techniques, we furnish an interpretation of the
multiplicity of a solution, in terms of positive distinct solutions of a
quasilinear equation on $\Omega$, approximating $(P_\varepsilon)$.
