Geodesic
Periodic solutions of degenerate differential equations in vector-valued function spaces
Carlos Lizama1 ; Rodrigo Ponce1
1 Departamento de Matemática Facultad de Ciencias Universidad de Santiago de Chile Casilla 307-Correo 2 Santiago, Chile
Studia Mathematica, Tome 202 (2011) no. 1, pp. 49-63 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $A$ and $M$ be closed linear operators defined on a complex Banach space $X.$ Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation $\frac{d}{dt}(Mu(t)) = Au(t) + f(t)$, in terms of either boundedness or $R$-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces.
DOI : 10.4064/sm202-1-3
Keywords: closed linear operators defined complex banach space using operator valued fourier multiplier theorems obtain necessary sufficient conditions existence uniqueness periodic solutions equation frac terms either boundedness r boundedness modified resolvent operator determined equation results obtained scales periodic besov periodic lebesgue vector valued spaces

Carlos Lizama 1 ; Rodrigo Ponce 1

1 Departamento de Matemática Facultad de Ciencias Universidad de Santiago de Chile Casilla 307-Correo 2 Santiago, Chile 
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Carlos Lizama; Rodrigo Ponce. Periodic solutions of degenerate differential equations in
vector-valued function spaces. Studia Mathematica, Tome 202 (2011) no. 1, pp. 49-63. doi: 10.4064/sm202-1-3

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