A class of degenerate elliptic eigenvalue problems

被引：6

作者：

Lucia, Marcello ^{[1
]}

Schuricht, Friedemann ^{[2
]}

机构：

[1] CUNY Coll Staten Isl, Dept Math, CSI, Staten Isl, NY 10314 USA

[2] Tech Univ Dresden, Fachbereich Math, D-01062 Dresden, Germany

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2013年 / 2卷 / 01期

关键词：

Nonlinear eigenvalue problems; quasilinear elliptic equations; critical point theory; convex analysis; nonsmooth analysis; CRITICAL-POINT THEORY; P-LAPLACE OPERATOR; 1-LAPLACE OPERATOR; INDEFINITE WEIGHT;

D O I：

10.1515/anona-2012-0202

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a general class of eigenvalue problems where the leading elliptic term corresponds to a convex homogeneous energy function that is not necessarily differentiable. We derive a strong maximum principle and show uniqueness of the first eigenfunction. Moreover we prove the existence of a sequence of eigensolutions by using a critical point theory in metric spaces. Our results extend the eigenvalue problem of the p-Laplace operator to a much more general setting.

引用

页码：91 / 125

页数：35

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