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Monotonicity and existence of periodic orbits for projected dynamical systems on Hilbert spaces

Author: Monica-Gabriela Cojocaru
Journal: Proc. Amer. Math. Soc. 134 (2006), 793-804
MSC (2000): Primary 34A36, 34C25, 49J40; Secondary 37N40, 34A60
Published electronically: July 21, 2005
MathSciNet review: 2180897
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Abstract: We present here results about the existence of periodic orbits for projected dynamical systems (PDS) under Minty-Browder monotonicity conditions. The results are formulated in the general context of a Hilbert space of arbitrary (finite or infinite) dimension. The existence of periodic orbits for such PDS is deduced by means of nonlinear analysis, using a fixed point approach. It is also shown how occurrence of periodic orbits is intimately related to that of critical points (equilibria) of a PDS in certain cases.

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Additional Information

Monica-Gabriela Cojocaru
Affiliation: Department of Mathematics and Statistics, MacNaughton Hall, Room 548, University of Guelph, Guelph, Ontario, Canada N1G 2W1

Received by editor(s): August 12, 2004
Received by editor(s) in revised form: October 6, 2004, and October 18, 2004
Published electronically: July 21, 2005
Additional Notes: This research was funded by NSERC Discovery Grant No. 045997.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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