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


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:
$$v'(t) = Av(t) + f(t),t \in R.$$


Banach Space Periodic Solution Exponential Growth Parabolic Equation Real Line 
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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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