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OMEGA LIMIT SETS IN POSITIVE CONES

Published online by Cambridge University Press:  23 December 2003

YONG-ZHUO CHEN
YONG-ZHUO CHEN
Affiliation:
Department of Mathematics, Computer Science and Engineering, University of Pittsburgh at Bradford, Bradford, PA 16701 USAyong@pitt.edu
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Abstract

The omega limit sets of a nonlinear operator $T$ which is defined on a positive cone and satisfies certain ray-contractive type conditions are discussed. Under the assumption that the restriction of $T$ to a compact subset is surjective, the following alternatives are proved: the omega limit set of a point in the cone either consists of a fixed point or forms a 2-cycle. In addition, new proofs and extensions to relevant results are given.

Keywords

47H0747H09
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 1 , January 2004 , pp. 72 - 80
Copyright
© The London Mathematical Society 2004

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