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(phi(1)(vertical bar del u vertical bar)del u) = Fu (x, u, v) in Omega, -div (phi(2) (vertical bar del v vertical bar)del v) = Fv (x, u, v) in Omega, u = v = 0 on partial derivative Omega, where Omega is a bounded domain in R-N (N >= 2) with smooth boundary partial derivative Omega, functions phi(i) (t)t (i = 1, 2) are increasing homeomorphisms from R+ onto R+. When F satisfies some (phi(1), phi(2)) -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. Appl., 426 (2015), 466-483]. (C) 2017 All rights reserved.