  We study a quasilinear elliptic problem $-\text{div} (\nabla \Phi(\nabla
u))+V(x)N'(u)=f(u)$ with anisotropic convex function $\Phi$ on whole
$\mathbb{R}^n$. To prove existence of a nontrivial weak solution we use
mountain pass theorem for a functional defined on anisotropic Orlicz-Sobolev
space $W^1 L^{\Phi}(\mathbb{R}^n)$. As the domain is unbounded we need to use
Lions type lemma formulated for Young functions. Our assumptions broaden the
class of considered functions $\Phi$ so our result generalizes earlier
analogous results proved in isotropic setting.
