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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Periodic solutions of degenerate differential equations in vector-valued function spaces

### Tom 202 / 2011

Studia Mathematica 202 (2011), 49-63 MSC: Primary 35K65; Secondary 34G10, 34K13. DOI: 10.4064/sm202-1-3

#### Streszczenie

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.

#### Autorzy

Casilla 307-Correo 2
Santiago, Chile
e-mail
• Rodrigo PonceDepartamento de Matemática