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 (a(1) (vertical bar del u vertical bar) del u) = lambda(1) F-u (x, u, v) - lambda(2) G(u) (x, u, v) - lambda(3) H-u (x, u, v) in Omega, -div (a(2) (vertical bar del u vertical bar) del u) = lambda(1) F-v (x, u, v) - lambda(2) G(v) (x, u, v) - lambda(3) H-v (x, u, v) in Omega, u = v = 0 on partial derivative Omega, where Omega is a bounded domain in R-N (N >= 1) with smooth boundary partial derivative Omega, lambda(1), lambda(2), lambda(3) are three parameters, phi(i) (t) = a(i) (vertical bar t vertical bar)t (i = 1, 2) are two increasing homeomorphisms from R onto R, and functions F, G, H are of class C-1 (Omega x R-2, R) and satisfy some reasonable growth conditions. By using a three critical points theorem due to B. Ricceri, we obtain that system has at least three solutions. With some additional conditions, by using a four critical points theorem due to G. Anello, we obtain that system has at least four solutions.