On a superquadratic elliptic system with strongly indefinite structure

In this paper, we consider the elliptic system-Δu=g(x,v)inΩ,-Δv=f(x,u)inΩ,u=v=0on∂Ω,where Ω is a bounded smooth domain in RN, and f and g satisfy a general superquadratic condition. By using variational methods, we prove the existence of infinitely many solutions. Our argument relies on the application of a generalized variant fountain theorem for strongly indefinite functionals. Previous results in the topic are improved.