Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

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

Verónica Pobletea1

a1 Departamento de Matemática, Facultad de Ciencia, Universidad de Santiago de Chile, Avenida Libertador Bernardo O'Higgins 3363, Santiago, Chile (vpoblete@lauca.usach.cl)

Abstract

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.

(Received July 07 2005)

Keywords

  • Primary 45N05;
  • Secondary 45D05;
  • 43A15;
  • integro-differential equation;
  • maximal regularity;
  • Fourier multiplier;
  • vector-valued periodic Besov space