Periodic solutions of an abstract third-order differential equation

Tom 215 / 2013

Verónica Poblete, Juan C. Pozo Studia Mathematica 215 (2013), 195-219 MSC: Primary 34G10; Secondary 34C25. DOI: 10.4064/sm215-3-1

Streszczenie

Using operator valued Fourier multipliers, we characterize maximal regularity for the abstract third-order differential equation $\alpha u'''(t) + u''(t) = \beta Au(t) +\gamma Bu'(t) +f(t)$ with boundary conditions $u(0)=u(2\pi )$, $u'(0)=u'(2\pi )$ and $u''(0)=u''(2\pi )$, where $A$ and $B$ are closed linear operators defined on a Banach space $X$, $\alpha ,\beta ,\gamma \in \mathbb {R}_+$, and $f$ belongs to either periodic Lebesgue spaces, or periodic Besov spaces, or periodic Triebel–Lizorkin spaces.

Autorzy

  • Verónica PobleteFacultad de Ciencias
    Universidad de Chile
    Las Palmeras 3425
    Santiago, Chile
    e-mail
  • Juan C. PozoFacultad de Economía y Empresa
    Universidad Diego Portales
    Avda. Santa Clara 797, Huechuraba
    Santiago, Chile
    e-mail

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