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primary 45n05

Proceedings of the Edinburgh Mathematical Society (1)

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SOLUTIONS OF SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATIONS ON PERIODIC BESOV SPACES
Verónica Poblete
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 2 / June 2007

Published online by Cambridge University Press:

17 May 2007, pp. 477-492
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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.