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Upper semi continuity of attractors of delay differential equations in the delay

Published online by Cambridge University Press:  17 April 2009

Peter E. Kloeden
Peter E. Kloeden
Affiliation:
FB Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main, Germany e-mail: kloeden@math.uni-frankfurt.de
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It is shown that if a retarded delay differential equation has a global attractor in the space C ([—τ0, ], ℝd) for a given nonzero constant delay τ0, then the equation has an attractor Aτ in the space C ([—τ, 0], ℝd) for nearby constant delays τ. Moreover the attractors Aτ converge upper semi continuously to in C ([—τ0, 0], ℝd) in the sense that they are identified through corresponding segments of entire trajectories in ℝd with nonempty compact subsets of C ([—τ0, 0], ℝd) which converge upper semi continuously to in C ([—τ0, 0], ℝd).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 2 , April 2006 , pp. 299 - 306
Copyright
Copyright © Australian Mathematical Society 2006

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