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

 

Nonzero positive solutions of systems of elliptic boundary value problems


Author: K. Q. Lan
Journal: Proc. Amer. Math. Soc. 139 (2011), 4343-4349
MSC (2010): Primary 35J57; Secondary 45G15, 47H10
Published electronically: April 4, 2011
MathSciNet review: 2823079
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Abstract: A new result on existence of nonzero positive solutions of systems of second order elliptic boundary value problems is obtained under some sublinear conditions involving the principle eigenvalues of the corresponding linear systems. Results on eigenvalue problems of such elliptic systems are derived and generalize some previous results on the eigenvalue problems of systems of Laplacian elliptic equations. Applications of our results are given to two such systems with specific nonlinearities.


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Additional Information

K. Q. Lan
Affiliation: Department of Mathematics, Ryerson University, Toronto, Ontario, Canada M5B 2K3
Email: klan@ryerson.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10840-2
PII: S 0002-9939(2011)10840-2
Keywords: Systems of elliptic boundary value problems, sublinear condition, nonzero positive solutions, fixed point index
Received by editor(s): June 30, 2010
Received by editor(s) in revised form: October 9, 2010
Published electronically: April 4, 2011
Additional Notes: The author was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.