Geodesic
Periodic solutions of an abstract third-order differential equation
Verónica Poblete1 ; Juan C. Pozo2
1 Facultad de Ciencias Universidad de Chile Las Palmeras 3425 Santiago, Chile
2 Facultad de Economía y Empresa Universidad Diego Portales Avda. Santa Clara 797, Huechuraba Santiago, Chile
Studia Mathematica, Tome 215 (2013) no. 3, pp. 195-219 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm215-3-1
Keywords: using operator valued fourier multipliers characterize maximal regularity abstract third order differential equation alpha beta gamma boundary conditions where closed linear operators defined banach space alpha beta gamma mathbb belongs either periodic lebesgue spaces periodic besov spaces periodic triebel lizorkin spaces

Verónica Poblete 1 ; Juan C. Pozo 2

1 Facultad de Ciencias Universidad de Chile Las Palmeras 3425 Santiago, Chile
2 Facultad de Economía y Empresa Universidad Diego Portales Avda. Santa Clara 797, Huechuraba Santiago, Chile 
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Verónica Poblete; Juan C. Pozo. Periodic solutions of an abstract
 third-order differential equation. Studia Mathematica, Tome 215 (2013) no. 3, pp. 195-219. doi: 10.4064/sm215-3-1

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