Resumen de Existence of Ground State Solutions for Kirchhoff Problems with Hardy Potential

MengYun Zhou, YongYi Lan

• 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.