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Almost Automorphic Functions in Frechet Spaces and Applications to Differential Equations

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Abstract

In this paper we first develop a theory of almost automorphic functions with values in Frechet spaces. Then, we consider the semilinear differential equation x'(t) = A x(t) + f(t, x(t)), t ∈ ℝ in a Frechet space X, where A is the infinitesimal generator of a C0-semigroup satisfying some conditions of exponential stability. Under suitable conditions on f, we prove the existence and uniqueness of an almost automorphic mild solution to the equation.

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Authors and Affiliations

  1. The University of Memphis, Department of Mathematical Sciences, Memphis, TN, 38152, USA

    Ciprian S. Gal

  2. Department of Mathematics, University of Oradea, Romania, 3700 Oradea, Romania

    Sorin G. Gal

  3. Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA

    Gaston M. N'Guerekata

Authors
  1. Ciprian S. Gal
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  2. Sorin G. Gal
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  3. Gaston M. N'Guerekata
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Corresponding authors

Correspondence to Ciprian S. Gal, Sorin G. Gal or Gaston M. N'Guerekata.

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Gal, C., Gal, S. & N'Guerekata, G. Almost Automorphic Functions in Frechet Spaces and Applications to Differential Equations. Semigroup Forum 71, 201–230 (2005). https://doi.org/10.1007/s00233-005-0508-y

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  • DOI: https://doi.org/10.1007/s00233-005-0508-y

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