In this paper, we investigate the following nonlinear and non-homogeneous elliptic
system:
⎧⎪⎨⎪⎩
– div(a1(|∇u|)∇u) + V1(x)a1(|u|)u = Fu(x, u, v) in RN,
– div(a2(|∇v|)∇v) + V2(x)a2(|v|)v = Fv(x, u, v) in RN,
(u, v) ∈ W1,1(RN) × W1,2(RN),
where φi(t) = ai(|t|)t(i = 1, 2) are two increasing homeomorphisms from R onto R,
functions Vi(i = 1, 2) and F are 1-periodic in x, and F satisfies some (φ1,φ2)-superlinear
Orlicz-Sobolev conditions. By using a variant mountain pass lemma, we obtain that
the system has a ground state.

EB00000002885K

Available

• Existence of ground state solutions for a class of quasilinear elliptic systems in Orlicz-Sobolev spaces