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Annali di Matematica Pura ed Applicata

, Volume 150, Issue 1, pp 67–117 | Cite as

Solvability on the real line of a class of linear volterra integrodifferential equations of parabolic type

  • Giuseppe Da Prato
  • Alessandra Lunardi
Article

Summary

We consider an abstract parabolic integrodifferential equation with infinite delay in general Banach space X:
$$u'(t) = Au(t) + \int\limits_{ - \infty }^t {K(t - s)u(s)ds + f(t),t \in R}$$
(*)
where A: D(A) ⊂ X → X generates an analytic semigroup, and K(t) ε L(D(A), X) for every t ⩾ 0. Under suitable assumptions on the kernel K, we extend to equation (*) the well known results about bounded solutions, periodic solutions, and solutions with exponential growth, of the abstract parabolic equation:
$$v'(t) = Av(t) + f(t),t \in R.$$
(**)

Keywords

Banach Space Periodic Solution Exponential Growth Parabolic Equation Real Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1987

Authors and Affiliations

  • Giuseppe Da Prato
    • 1
  • Alessandra Lunardi
    • 2
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di MatematicaPisaItaly

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