Ground State Solution for the Logarithmic Schrödinger–Poisson System with Critical Growth

• Yaqing Cai ^[1] ; Yulin Zhao ^[1]
  1. [1] Hunan University of Technology

     Hunan University of Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
• Idioma: inglés
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• Resumen

  • In this paper we investigate a class of logarithmic Schrödinger–Poisson system with critical growth which are from physically relevant backgrounds. Under suitable assumptions on the potential V(x), we obtain the existence of ground state solution for ε > 0 sufficiently small via using a constrained minimization on a Nehari manifold and some new techniques. Specially, by restricting the least energy c to a suitable interval, we overcome some difficulties brought by the critical term u5 for restoring the compactness of the minimizing sequence of the least energy c.