ON THE STRUCTURE OF THE SECOND EIGENFUNCTIONS OF THE p-LAPLACIAN ON A BALL

被引：13

作者：

Anoop, T. V. ^{[1
]}

Drabek, P. ^{[2
,3
]}

Sasi, Sarath ^{[4
]}

机构：

[1] Indian Inst Technol Madras, Dept Math, Chennai 36, Tamil Nadu, India

[2] Univ W Bohemia, Fac Sci Appl, Dept Math, Univ 8, Plzen 30614, Czech Republic

[3] Univ W Bohemia, Fac Sci Appl, NTIS, Univ 8, Plzen 30614, Czech Republic

[4] Natl Inst Sci Educ & Res, Sch Math Sci, Jatni 752050, Odisha, India

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 06期

关键词：

p-Laplacian; nonlinear eigenvalue problem; symmetry properties; shape derivative; variational characterization; EIGENVALUE;

D O I：

10.1090/proc/12902

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove that the second eigenfunctions of the p-Laplacian, p > 1, are not radial on the unit ball in R-N, for any N >= 2. Our proof relies on the variational characterization of the second eigenvalue and a variant of the deformation lemma. We also construct an infinite sequence of eigenpairs {tau(n),.Psi(n)} such that Psi(n) is nonradial and has exactly 2n nodal domains. A few related open problems are also stated.

引用

页码：2503 / 2512

页数：10

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