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

• Wang, Lin-Jing ^[1] ; Li, Gui-Dong ^[1] ; Tang, Chun-Lei ^[1]
  1. [1] Southwest University

     Southwest University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
• Idioma: inglés
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• Resumen

  • 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.