含Hardy位势的椭圆型方程特征值问题

Eigenvalue Problems of Elliptic PDEs with Hardy Potential

考虑含Hardy位势:1/|x|2,N≥3;1/(|x|lnR/|x|)2,N=2,的椭圆型偏微分方程的特征值问题.在空间H01(Ω)中该问题解的存在性已有文献给出了一个(近乎)充分必要条件,但我们在一个新空间中证明了它的可解性。

Eigenvallue problems of elliptic partial differential equations with Hardy potential are considered： 1/│x│^2, N/〉 3 ; 1/（ │x│^2 InR/│x│^2, N = 2. It shows that necessary conditions are given to the solution of these problems in H0^1 （Ω） . A solution has been proved in a new space.