Existence and multiplicity of solutions for a class of quasilinear elliptic systems in Orlicz-Sobolev spaces

In this paper, we investigate the following nonlinear and non-homogeneous elliptic system -div( ϕ1(|∇u|)∇u) = Fu(x, u, v) in Ω, -div( ϕ2(|∇v|)∇v) = Fv(x, u, v) in Ω, u = v = 0 on ∂Ω, where Ω is a bounded domain in R^N(N≥2) with smooth boundary ∂Ω, functions φi(t)t (i = 1, 2) are increasing homeomor- phisms from R^+ onto R^+. When F satisfies some (φ1, φ2)-superlinear and subcritical growth conditions at infinity, by using the mountain pass theorem we obtain that system has a nontrivial solution, and when F satisfies an additional symmetric condition, by using the symmetric mountain pass theorem, we obtain that system has infinitely many solutions. Some of our results extend and improve those corresponding results in Carvalho et al. [M. L. M. Carvalho, J. V. A. Goncalves, E. D. da Silva, J. Math. Anal. 6 (2015), 466–483].