Schrödinger–Bopp–Podolsky System with Steep Potential Well

• Qiutong Zhu ^[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. 22, Nº 4, 2023
• Idioma: inglés
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• Resumen

  • In this paper, we study the following Schrödinger–Bopp–Podolsky system:

    −u + λV(x)u + q2ϕu = f (u) −ϕ + a22ϕ = 4πu2, where u, ϕ : R3 → R, a > 0, q > 0, λ is real positive parameter, f satisfies supper 2 lines growth. V ∈ C(R3, R), which suppose that V(x) repersents a potential well with the bottom V −1(0). There are no results of solutions for the system with steep potential well in the current literature because of the presence of the nonlocal term. Throughout the truncation technique and the parameter-dependent compactness lemma, we get a poistive energy solution uλ,q for λ large and q small. In the last part, we explore the asymptotic behavior as q → 0, λ → +∞.