Existence and multiplicity of solutions for asymptotically Hamiltonian elliptic systems in RNRN

This paper is concerned with the following nonperiodic Hamiltonian elliptic system{−△u+V(x)u=Hu(x,u,v)in RN,−△v+V(x)v=−Hv(x,u,v)in RN,u(x)→0andv(x)→0as |x|→∞, where the potential V is bounded below, and H is asymptotically linear in z   as |z|→∞|z|→∞ with z=(u,v)z=(u,v). By applying a generalized linking theorem of strongly indefinite functionals, we obtain solutions for the above system.