Existence and multiplicity of semiclassical solutions for asymptotically Hamiltonian elliptic systems

This paper is concerned with the following nonperiodic Hamiltonian elliptic system { − ε 2 △ u + V ( x ) u = H u ( x , u , v ) in R N , − ε 2 △ v + V ( x ) v = − H v ( x , u , v ) in R N , u ( x ) → 0 and v ( x ) → 0 as | 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.