Geodesic
A stability theorem for convergence of a Lyapounov function along trajectories of nonexpansive semigroups
Electronic journal of differential equations, Tome 2006 (2006)
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.
Classification : 47H05, 47H20
Keywords: monotone, semigroup, lyapounov function 
@article{EJDE_2006__2006__a144,
     author = {Choudhary,  Renu},
     title = {A stability theorem for convergence of a {Lyapounov} function along trajectories of nonexpansive semigroups},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1115.47045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a144/}
}
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Choudhary,  Renu. A stability theorem for convergence of a Lyapounov function along trajectories of nonexpansive semigroups. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a144/