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

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 pro...

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Bibliographic Details
Published inCommunications on pure and applied mathematics Vol. 68; no. 6; pp. 1014 - 1065
Main Authors Berestycki, Henri, Rossi, Luca
Format Journal Article
LanguageEnglish
Published New York Blackwell Publishing Ltd 01.06.2015
John Wiley and Sons, Limited
Subjects
Dirichlet problem
Eigenvalues
Validity
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Summary: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. © 2015 Wiley Periodicals, Inc.
Bibliography:ark:/67375/WNG-L1L9T4WS-G
ArticleID:CPA21536
istex:6443D0134A36BF0293CC470941DE7A3F72A169FB
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21536