In this talk we consider the $\phi\,$-Laplacian problem with Dirichlet boundary condition,
$$\left\{
\begin{array}{ll}
-{\rm div}\left(\phi(|\nabla u|)\frac{\nabla u}{|\nabla u|}\right)=\lambda\,g(\cdot)\,\phi(u)\,\,\,\mbox{in}\,\,\,\Omega,\,\lambda\in\re,\\\vspace{-.1in}
\\
u\vert_{\partial\Omega}=0.\\
\end{array}%
\right.$$
The term $\phi$ is a real odd and increasing homeomorphism, $g$ is a nonnegative function in $L^{\infty}(\Omega)$ and $\Omega\subseteq\mathbb{R}^N$ is a bounded domain. We analyze the asymptotic behavior of sequences of eigenvalues of the differential equation under mild hypotheses. The treatment is based solely on convergence assumptions on the associated sequence of eigenfunctions. We assume that the latter is asymptotic to either zero or infinity (in a precise sense). The core result of these notes establishes that the liminf of the associated sequence of eigenvalues coincides with the first eigenvalue of the usual $p$-Laplace operator. Moreover, we demonstrate that any weak-$\star$ limit of the eigenfunctions is an associated ground state.