Resumen de The Concentration of Multiplicity Solutions for a Class Hamiltonian Elliptic Systems

Yuanyang Yu

• In this paper, we are concerned with the concentration of multiplicity solutions for the following Hamiltonian elliptic systems −ε2u + u = K(x) f (v), x ∈ RN , −ε2v + v = K(x)g(u), x ∈ RN , where N ≥ 3, ε > 0 is a small parameter, K : RN → R is bounded positive continuous function, f and g are continuous but are not necessarily of class C1. 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.