含奇性拟线性椭圆型方程的特征值问题

Eigenvalue problem for singular quasilinear elliptic equation

讨论奇性拟线性椭圆型方程的特征值问题,其中,第一特征值对应的特征函数是C1,α(Ω)相关的,而且是正的、单一的、孤立的,且关于非负特征函数是唯一的正特征值。此外,这些性质也被推广到更一般的奇性情况。

The problem of eigenvalues and eigenfunctions of a quasilinear elliptic equation involving singu- larity is studied. The first eigenvalue is associated to a C1,α（Ω） eigenfunction which is positive and unique, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive ei- genvalue associated to a non--negative eigenfunction. Furthermore, these properties are extended to more general situations.