In this paper,we consider the eigenvalue problem of the singular differential equation-Δu_(i)-h/|x|^(2) u_(i)+V(x)u_(i)=λ_(i)(V,h)u_(i) in a bounded open ball with Dirichlet boundary condition in 3-dimensional space...In this paper,we consider the eigenvalue problem of the singular differential equation-Δu_(i)-h/|x|^(2) u_(i)+V(x)u_(i)=λ_(i)(V,h)u_(i) 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 constant}.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.展开更多
文摘In this paper,we consider the eigenvalue problem of the singular differential equation-Δu_(i)-h/|x|^(2) u_(i)+V(x)u_(i)=λ_(i)(V,h)u_(i) 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 constant}.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.
