Ground State Sign-Changing Solutions for a Schrödinger–Poisson System with Steep Potential Well and Critical Growth

• Xiao-Qing Huang ^[1] ; Jia-Feng Liao ^[1] ; Rui-Qi Liu ^[2]
  1. [1] China West Normal University

     China West Normal University

     China

     
  2. [2] Meishan High School, Meishan
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 2, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this article, we consider the existence of ground state sign-changing solutions to a class of Schrödinger–Poisson systems −u + Vλ(x)u + φu = |u| 4u + μ f (u), in R3, −φ = u2, in R3, where μ > 0 and Vλ(x) = λV(x) + 1 with λ > 0. Under suitable conditions on f and V, by using the constraint variational method and quantitative deformation lemma, we prove that the above problem has one ground state sign-changing solution and the energy of ground state sign-changing solution is strictly more than twice the energy of the ground state solution. Furthermore, we also study the asymptotic behavior of ground state sign-changing solutions as λ → ∞.

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