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SOLUTIONS OF SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATIONS ON PERIODIC BESOV SPACES

Published online by Cambridge University Press:  17 May 2007

Verónica Poblete
Affiliation:
Departamento de Matemática, Facultad de Ciencia, Universidad de Santiago de Chile, Avenida Libertador Bernardo O'Higgins 3363, Santiago, Chile (vpoblete@lauca.usach.cl)
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Abstract

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Maximal regularity for an integro-differential equation with infinite delay on periodic vector-valued Besov spaces is studied. We use Fourier multipliers techniques to characterize periodic solutions solely in terms of spectral properties on the data. We study a resonance case obtaining a compatibility condition which is necessary and sufficient for the existence of periodic solutions.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2007