%0 Journal Article
%T The eigenvalue problem for a singular quasilinear elliptic equation
%A Benjin Xuan
%J Electronic Journal of Differential Equations
%D 2004
%I Texas State University
%X We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega)$ eigenfunction which is positive and unique (up to a multiplicative constant), that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.
%K Singular quasilinear elliptic equation
%K eigenvalue problem
%K Caffarelli-Kohn-Nirenberg inequality.
%U http://ejde.math.txstate.edu/Volumes/2004/16/abstr.html