  In this paper, we analyze an eigenvalue problem for quasi-linear elliptic
operators involving homogeneous Dirichlet boundary conditions in a open smooth
bounded domain. We show that the eigenfunctions corresponding to the
eigenvalues belong to $L^{\infty}$, which implies $C^{1,\alpha}$ smoothness,
and the first eigenvalue is simple. Moreover, we investigate the bifurcation
results from trivial solutions using the Krasnoselski bifurcation theorem and
from infinity using the Leray-Schauder degree. We also show the existence of
multiple critical points using variational methods and the Krasnoselski genus.
