Electron. J. Diff. Eqns., Vol. 2004(2004), No. 64, pp. 1-18.

A limit set trichotomy for order-preserving systems on time scales

Christian Poetzsche & Stefan Siegmund

In this paper we derive a limit set trichotomy for abstract order-preserving 2-parameter semiflows in normal cones of strongly ordered Banach spaces. Additionally, to provide an example, Muller's theorem is generalized to dynamic equations on arbitrary time scales and applied to a model from population dynamics.

Submitted April 15, 2004. Published April 27, 2004.
Math Subject Classifications: 37C65, 37B55, 92D25.
Key Words: Limit set trichotomy, 2-parameter semiflow, dynamic equation, time scale.

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Christian Poetzsche
University of Augsburg, Department of Mathematics
86135 Augsburg, Germany
email: poetzsche@math.uni-augsburg.de
Stefan Siegmund
J. W. Goethe University, Department of Mathematics
60325 Frankfurt, Germany
email: siegmund@math.uni-frankfurt.de

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