In this paper, we shall be concerned with the existence result of the following
problem,
− u div = 0 on (a(x∂, , u, ∇u)) − div((x, u)) = f in , (0.1)
with the second term f belongs to L1(). The growth and the coercivity conditions on
the monotone vector field a are prescribed by a generalized N-function M. We assume
any restriction on M, therefore we work with Musielak–Orlicz spaces which are not
necessarily reflexive. The lower order term  is a Carathéodory function satisfying
only a growth condition.

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• Entropy solution for a nonlinear elliptic problem with lower order term in Musielak–Orlicz spaces