Electron. J. Diff. Eqns., Vol. 2006(2006), No. 120, pp. 1-10.

A stability theorem for convergence of a lyapounov function along trajectories of nonexpansive semigroups

Renu Choudhary

It is known that a regularly Lyapounov function for a semigroup of contractions on a Hilbert space converges to its minimum along the trajectories of the semigroup. In this paper we show that this Lyapounov function nearly converges to its minimum along trajectories of the semigroup generated by a small bounded perturbation of the semigroup generator.

Submitted July 28, 2005. Published October 2, 2006.
Math Subject Classifications: 47H05, 47H20.
Key Words: Monotone; semigroup; Lyapounov function.

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Renu Choudhary
Department of Mathematics
University of Auckland
Private Bag 92019, Auckland, New Zealand
email: renu@math.auckland.ac.nz

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