A note on non-existence results for semi-linear cooperative elliptic systems via moving spheres
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- by Henghui Zou PDF
- Proc. Amer. Math. Soc. 134 (2006), 1635-1646 Request permission
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
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984. Corrected reprint of the 1967 original. MR 762825, DOI 10.1007/978-1-4612-5282-5
- Wolfgang Reichel and Henghui Zou, Non-existence results for semilinear cooperative elliptic systems via moving spheres, J. Differential Equations 161 (2000), no. 1, 219–243. MR 1740363, DOI 10.1006/jdeq.1999.3700
- Zou, H., A priori estimates and existence for strongly-coupled semi-linear cooperative elliptic systems, Comm. PDE, accepted.
Additional Information
- Henghui Zou
- Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294
- Received by editor(s): November 1, 2004
- Published electronically: January 4, 2006
- Communicated by: David S. Tartakoff
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2204274