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ftp ejde.math.txstate.edu (login: ftp) THE EIGENVALUE PROBLEM FOR A SINGULAR QUASILINEAR ELLIPTIC EQUATION

By Benjin Xuan

Abstract

Abstract. We show that many results about the eigenvalues and eigenfunc-tions 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 as-sociated 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. 1

Year: 2014
OAI identifier: oai:CiteSeerX.psu:10.1.1.485.3923
Provided by: CiteSeerX
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