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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Discreteness and simplicity of the spectrum of a quasilinear Sturm-Liouville-type problem on an infinite interval


Authors: Pavel Drábek and Alois Kufner
Journal: Proc. Amer. Math. Soc. 134 (2006), 235-242
MSC (2000): Primary 34L05, 47E05, 34B40
Published electronically: June 13, 2005
MathSciNet review: 2170563
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Abstract: We present sufficient conditions on the coefficients to get the discreteness and simplicity of the spectrum of a quasilinear Sturm-Liouville-type problem on an infinite interval. This condition appears to be necessary and sufficient for the compact embedding of certain weighted spaces. Our result generalizes those which are known from linear theory.


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Additional Information

Pavel Drábek
Affiliation: Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic
Email: pdrabek@kma.zcu.cz

Alois Kufner
Affiliation: Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic
Email: kufner@math.cas.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07958-X
PII: S 0002-9939(05)07958-X
Keywords: Discreteness of the spectrum, compact embeddings of the weighted spaces, minimax principles
Received by editor(s): February 25, 2004
Received by editor(s) in revised form: August 30, 2004
Published electronically: June 13, 2005
Additional Notes: This research was supported by the Grant Agency of the Czech Republic, grant No. 201/03/0671, and by the Grant Agency of the Academy of Sciences of the Czech Republic, grant No. A1019305.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.