The Eigenvalue Problem of a Singular Quasilinear Elliptic Equation

In this paper, we shall study the eigenvalue problem of a singular quasilinear elliptic equation. We will show that many results about the eigenvalues and eigenfunctions in the non-singular case can be extended to the more general singular case, e.g., the first eigenvalue λ is associated to a (Ω) eigenfunction which is positive in Ω and unique (up to a multiplicative constant), that is, λ is simple. Moreover λ is isolated, and is the unique positive eigenvalue associated to a non-negative eigenfunction, and some variational properties of the second eigenvalue λ