Xuan, Benjin2021-04-052021-04-052004-02-06Xuan, B. (2004). The eigenvalue problem for a singular quasilinear elliptic equation. <i>Electronic Journal of Differential Equations, 2004</i>(16), pp. 1-11.1072-6691https://hdl.handle.net/10877/13335We 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 C1,α(Ω) 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.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalSingular quasilinear elliptic equationEigenvalue problemCaffarelli-Kohn-Nirenberg inequalityArticle