Existence and Concentration of Ground State Solutions for a Schrödinger–Poisson-Type System with Steep Potential Well

• Jianwen Huang ^[1] ; Chunfang Chen ^[1] ; Chenggui Yuan ^[2]
  1. [1] Nanchang University

     Nanchang University

     China

     
  2. [2] Swansea University

     Swansea University

     Castle, Reino Unido

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 2, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we study the following nonlocal problem in R3 −u + (1 + λV(x))u − μφu = f (x, u), in R3, −φ = u2, in R3, where λ > 0 is a real parameter and μ > 0 is small enough. Under some suitable assumptions on V(x) and f (x, u), we prove the existence of ground state solutions for the problem when λ is large enough via variational methods. In addition, the concentration behavior of these ground state solutions is also investigated as λ → +∞.