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A note on non-existence results for semi-linear cooperative elliptic systems via moving spheres
Author:
Henghui Zou
Journal:
Proc. Amer. Math. Soc. 134 (2006), 1635-1646
MSC (2000):
Primary 35J55; Secondary 35J65
Posted:
January 4, 2006
MathSciNet review:
2204274
Full-text PDF Free Access
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Additional Information
Abstract: In this note, we extend some earlier non-existence, monotonicity and one-dimensionality results of W. Reichel and the author, by replacing the local Lipschitz continuity hypothesis on the non-linearities by a so-called boundedly uniform Lipschitz condition in the magnitude of  .
References
- 1.
Protter, M.H. and H.F. Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984. MR 0762825 (86f:35034)
- 2.
Reichel, W. and H. Zou, Non-existence results for semilinear cooperative elliptic systems via moving spheres, J. Differential Eqs., 161(2000), pp.219-243. MR 1740363 (2000m:35066)
- 3.
Zou, H., A priori estimates and existence for strongly-coupled semi-linear cooperative elliptic systems, Comm. PDE, accepted.
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Additional Information
Henghui Zou
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08523-6
PII:
S 0002-9939(06)08523-6
Keywords:
Non-existence,
moving spheres,
cooperative,
maximum principles
Received by editor(s):
November 1, 2004
Posted:
January 4, 2006
Communicated by:
David S. Tartakoff
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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