Existence of Ground State Solutions for Kirchhoff Problems with Hardy Potential

• MengYun Zhou ^[1] ; YongYi Lan ^[1]
  1. [1] Jimei University

     Jimei University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 4, 2023
• Idioma: inglés
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• Resumen

  • This study is concerned with the following Kirchhoff problem:

    − a + b R3 |∇u| 2dx u − μ |x| 2 u = g(u) in R3\{0}, (A) where a, b > 0 are constants, μ < 1 4 . 1 |x| 2 is called the Hardy potential and g :

    R → R is a continuous function that satisfies the Berestycki–Lion type condition.

    Using variational methods, we establish two existence results for problem (A) under different conditions for g. Furthermore, if μ < 0, we prove that the mountain pass level in H1(R3) can not be achieved.