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On Principal Eigenvalues for Indefinite Problems in Euclidean Space
Author(s) -
Rozenblum Grigori,
Solomyak Michael
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981920112
Subject(s) - mathematics , eigenvalues and eigenvectors , eigenfunction , euclidean space , sign (mathematics) , pure mathematics , spectrum of a matrix , principal (computer security) , space (punctuation) , weight function , euclidean geometry , mathematical analysis , function (biology) , matrix differential equation , geometry , differential equation , quantum mechanics , physics , computer science , operating system , linguistics , philosophy , evolutionary biology , biology
For the eigenvalue problem—λΔ u = q ( x ) u in IR d , with the weight function q changing sign, conditions are discussed for existence of eigenvalues with positive decaying eigenfunctions.