Stability and instability of radial standing waves to NLKG equation with an inverse-square potential

In this paper, we consider radial standing waves to a nonlinear Klein-Gordon equation with a repulsive inverse-square potential. It is known that existence of a "radial" ground state to the stationary problem of the nonlinear Klein-Gordon equation. Here, the "radial" ground state is a solution with the least energy among radial solutions to the stationary problem. We deal with stability and instability of the standing wave for the "radial" ground state.