Resumen de Existence and Concentration of Semi-classical Ground State Solutions for Chern–Simons–Schrödinger System

Lin-Jing Wang, Gui-Dong Li, Chun-Lei Tang

• In this paper, we consider the equation −ε2u + V(x)u + A0(u) + A2 1(u) + A2 2(u) u = f (u) in H1(R2), where ε is a small parameter, V is the external potential, Ai(i = 0, 1, 2) is the gauge field and f ∈ C(R, R) is 5-superlinear growth. By using variational methods and analytic technique, we prove that this system possesses a ground state solution uε.

  Moreover, our results show that, as ε → 0, the global maximum point xε of uε must concentrate at the global minimum point x0 of V.