Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains

被引：61

作者：

Berestycki, Henri ^{[1
]}

Rossi, Luca ^{[2
]}

机构：

[1] CAMS Ecole Hautes Etud Sci Sociales, F-75013 Paris, France

[2] Univ Padua, Dipartimento Matemat, I-35121 Padua, Italy

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2015年 / 68卷 / 06期

基金：

美国国家科学基金会; 欧洲研究理事会;

关键词：

SCHRODINGER-OPERATORS; POSITIVE SOLUTIONS; EQUATIONS; BOUNDARY; BEHAVIOR; FORM;

D O I：

10.1002/cpa.21536

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using three different notions of the generalized principal eigenvalue of linear second-order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the existence of positive eigenfunctions for the Dirichlet problem. Relations between these principal eigenvalues, their simplicity, and several other properties are further discussed. (c) 2015 Wiley Periodicals, Inc.

引用

页码：1014 / 1065

页数：52

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