A right inverse of differential operator $\Delta +a$ in weighted Hilbert space $L^2({\mathbb{R}}^n,e^{-|x{|}^2})$

Shaoyu Dai, Yang Liu, Yifei Pan

In this note, we prove the existence of weak solutions of a Poisson type equation in the weighted Hilbert space $L^2({\mathbb{R}}^n,e^{-|x{|}^2})$.