Strongly nonlinear periodic parabolic equation in Orlicz spaces

In this paper, we prove the existence of a weak solution to the following nonlinear periodic parabolic equations in Orlicz-spaces: partial derivative u/partial derivative t - div(a(x, t, del u)) = f(x, t) where -div(a(x, t, del u)) is a Leray-Lions operator defined on a subset of W-0(1,x) L-M(Q). The O2-condition is not assumed and the data f belongs to W E--1,x(M)(Q). The Galerkin method and the fixed point argument are employed in the proof.