Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces

Volume 168 / 2005

Valentin Keyantuo, Carlos Lizama Studia Mathematica 168 (2005), 25-50 MSC: Primary 45N05, 35K90; Secondary 45K05, 45D05, 46N20. DOI: 10.4064/sm168-1-3

Abstract

We use Fourier multiplier theorems to establish maximal regularity results for a class of integro-differential equations with infinite delay in Banach spaces. Concrete equations of this type arise in viscoelasticity theory. Results are obtained for periodic solutions in the vector-valued Lebesgue and Besov spaces. An application to semilinear equations is considered.

Authors

  • Valentin KeyantuoDepartment of Mathematics
    Faculty of Natural Sciences
    University of Puerto Rico
    P.O. Box 23355
    Puerto Rico 00931, U.S.A.
    e-mail
  • Carlos LizamaDepartamento de Matemática
    Facultad de Ciencias
    Universidad de Santiago de Chile
    Casilla 307, Correo 2
    Santiago, Chile
    e-mail

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