On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions

Abstract

The purpose of this paper is to investigate the existence and asymptotic properties of solutions to a Kirchhoff-type equation with Hardy potential and Berestycki–Lions conditions. Firstly, we show that the equation has a positive radial ground-state solution uλ by using the Pohozaev manifold. Secondly, we prove that the solution uλn, up to a subsequence, converges to a radial ground-state solution of the corresponding limiting equations as λn→0−. Finally, we provide a brief summary.