Abstract
In this paper we prove an existence result for some class of
variational boundary value problems for quasilinear elliptic equations
in the Musielak-Orlicz spaces $W^mL_\varphi(\Omega)$, under the
assumption that the conjugate function of $\varphi$ satisfies the
$\Delta_2$ condition. An imbedding theorem has also been provided
without assuming this condition.