On smoothness of carrying simplices

Author:
Janusz Mierczynski

Journal:
Proc. Amer. Math. Soc. **127** (1999), 543-551

MSC (1991):
Primary 34C30, 34C35; Secondary 58F12, 92D40

MathSciNet review:
1606000

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Abstract: We consider dissipative strongly competitive systems of ordinary differential equations. It is known that for a wide class of such systems there exists an invariant attracting hypersurface , called the carrying simplex. In this note we give an amenable condition for to be a submanifold-with-corners. We also provide conditions, based on a recent work of M. Benaïm (*On invariant hypersurfaces of strongly monotone maps*, J. Differential Equations **136** (1997), 302-319), guaranteeing that is of class .

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Additional Information

**Janusz Mierczynski**

Affiliation:
Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiań- skiego 27, PL-50-370 Wrocław, Poland

Email:
mierczyn@banach.im.pwr.wroc.pl

DOI:
https://doi.org/10.1090/S0002-9939-99-04887-X

Received by editor(s):
June 2, 1997

Additional Notes:
The author’s research was supported by KBN grant 2 P03A 076 08 (1995–97).

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1999
American Mathematical Society