Focusing nonlinear Hartree equation with inverse‐square potential

Abstract

AbstractIn this paper, we consider the scattering theory of the radial solution to focusing energy‐subcritical Hartree equation with inverse‐square potential in the energy space using the method from [4]. The main difficulties are due to the fact that the equation is not space‐translation invariant and that the nonlinearity is non‐local. Using the radial Sobolev embedding and a virial‐Morawetz type estimate we can exclude the concentration of mass near the origin. Besides, we can overcome the weak dispersive estimate when , using the dispersive estimate established by [23].