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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
DOI: https://doi.org/10.1090/S0002-9939-06-08523-6
Published electronically: January 4, 2006
MathSciNet review: 2204274
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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 $ \mathbf{u}$.


References [Enhancements On Off] (What's this?)

  • 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: https://doi.org/10.1090/S0002-9939-06-08523-6
Keywords: Non-existence, moving spheres, cooperative, maximum principles
Received by editor(s): November 1, 2004
Published electronically: January 4, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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