  We are concerned with a class of second order quasilinear elliptic equations
driven by a nonhomogeneous differential operator introduced by C.A. Stuart and
whose study is motivated by models in Nonlinear Optics. We establish sufficient
conditions for the existence of at least one or two non-negative solutions. Our
analysis considers the cases when the reaction has either a sublinear or a
linear growth. In the sublinear case, we also prove a nonexistence property.
The proofs combine energy estimates and variational methods. In particular, the
monotonicity trick is applied in order to overcome the lack of a priori bounds
on the Palais-Smale sequences.
