Radial groundstate solution for Schrödinger equation with Yukawa type instantaneous self-interaction

Abstract

In this paper, we consider the Schrödinger equation with Yukawa type instantaneous self-interaction. This equation arises in the quantum theory for Boson star. Motivated by the physical interest, we study the existence of radial decreasing groundstate solution for the above equation. Our results extend the study of Coulomb type instantaneous self-interaction to Yukawa type instantaneous self-interaction.