Generalized eigenvalue problems for (p, q)-Laplacian with indefinite weight

被引：50

作者：

Tanaka, Mieko ^{[1
]}

机构：

[1] Tokyo Univ Sci, Dept Math, Shinjyuku Ku, Tokyo 1628601, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 419卷 / 02期

关键词：

Indefinite weight; Nonlinear eigenvalue problems (p; q)-Laplacian; Mountain pass theorem; Global minimizer; EXISTENCE; LAPLACIAN;

D O I：

10.1016/j.jmaa.2014.05.044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents existence and non-existence results on a positive solution for quasilinear elliptic equations of the form u u = Amr (x) jur2u in Q with 1 < r r* < oo and i > 0, under Dirichlet boundary condition, where is a bounded domain in IP' and mr is a weight function in L' (0) admitting sign-change. We show that existence and non-existence of a positive solution depend only on the relation between A and the first eigenvalue of r-Laplacian with weight function mr, whence it is independent of the operator A, and the parameter A> 0. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1181 / 1192

页数：12

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