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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

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.