Existence and multiplicity of semiclassical solutions for asymptotically Hamiltonian elliptic systems

This paper is concerned with the following nonperiodic Hamiltonian elliptic system {−ε2△u+V(x)u=Hu(x,u,v)inRN,−ε2△v+V(x)v=−Hv(x,u,v)inRN,u(x)→0andv(x)→0as|x|→∞, where ε>0 is a small parameter, and the potential V is bounded below, and H is asymptotically linear in z as |z|→∞ with z=(u,v). By applying a generalized linking theorem of strongly indefinite functionals, we obtain the existence of multiple semiclassical solutions for the above system.