Abstract
In this paper,we consider the eigenvalue problem of the singular differential equation-△ui-h/|x|2ui+V(x)ui=λi(V,h)ui in a bounded open ball with Dirichlet boundary condition in 3-dimensional space,where,V ∈(V)={a ∈ L∞(Ω)|0≤a≤M a.e.,M is a given con-stant}.And we have made a detailed characterization of the weak solution space.Furthermore,the existence of the minimum eigenvalue and the fundamental gap are provided.