The Concentration of Multiplicity Solutions for a Class Hamiltonian Elliptic Systems

In this paper, we are concerned with the concentration of multiplicity solutions for the following Hamiltonian elliptic systems - ε 2 Δ u + u = K ( x ) f ( v ) , x ∈ R N , - ε 2 Δ v + v = K ( x ) g ( u ) , x ∈ R N , where N ≥ 3 , ε > 0 is a small parameter, K : R N → R is bounded positive continuous function, f and g are continuous but are not necessarily of class C 1 . By establishing a strongly indefinite variational setting, we prove the number of solutions is at least the number of global maximum points of K , and the maximum points of K is the concentration position of these solutions as ε → 0 .