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2 results

  • Maximal regularity for degenerate differential equations with infinite delay in periodic vector-valued function spaces

  • Carlos Lizama, Rodrigo Ponce
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013
    Published online by Cambridge University Press:
    21 August 2013, pp. 853-871
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  • Let A and M be closed linear operators defined on a complex Banach space X and let a ∈ L1(ℝ+) be a scalar kernel. We use operator-valued Fourier multipliers techniques to obtain necessary and sufficient conditions to guarantee the existence and uniqueness of periodic solutions to the equation

    with initial condition Mu(0) = Mu(2π), solely in terms of spectral properties of the data. Our results are obtained in the scales of periodic Besov, Triebel–Lizorkin and Lebesgue vector-valued function spaces.

  • ON DISCONTINUOUS FUNCTIONAL VOLTERRA INTEGRAL EQUATIONS AND IMPULSIVE DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES

  • S. HEIKKILÄ, D. O'REGAN
  • Journal:
    Glasgow Mathematical Journal / Volume 46 / Issue 3 / September 2004
    Published online by Cambridge University Press:
    11 October 2004, pp. 529-536
    Print publication:
    September 2004
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  • In this paper we apply fixed point results in ordered spaces to derive existence and comparison results for discontinuous functional integral equations of Volterra type in ordered Banach spaces. The results obtained are then applied to first order impulsive differential equations.