The eigenvalue problem for a singular quasilinear elliptic equation

Date

2004-02-06

Authors

Xuan, Benjin

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

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 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.

Description

Keywords

Singular quasilinear elliptic equation, Eigenvalue problem, Caffarelli-Kohn-Nirenberg inequality

Citation

Xuan, B. (2004). The eigenvalue problem for a singular quasilinear elliptic equation. <i>Electronic Journal of Differential Equations, 2004</i>(16), pp. 1-11.

Rights

Attribution 4.0 International

Rights Holder

Rights License