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• W2000549968 abstract "Operator-valued Fourier multipliers are used to study well-posedness of integro-differential equations in Banach spaces. Both strong and mild periodic solutions are considered. Strong well-posedness corresponds to maximal regularity which has proved very efficient in the handling of nonlinear problems. We are concerned with a large array of vector-valued function spaces: Lebesgue–Bochner spaces Lp, the Besov spaces Bp,qs (and related spaces such as the Hölder–Zygmund spaces Cs) and the Triebel–Lizorkin spaces Fp,qs. We note that the multiplier results in these last two scales of spaces involve only boundedness conditions on the resolvents and are therefore applicable to arbitrary Banach spaces. The results are applied to various classes of nonlinear integral and integro-differential equations." @default.
• W2000549968 created "2016-06-24" @default.
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• W2000549968 date "2009-02-01" @default.
• W2000549968 modified "2023-09-30" @default.
• W2000549968 title "Periodic solutions of integro-differential equations in vector-valued function spaces" @default.
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• W2000549968 doi "https://doi.org/10.1016/j.jde.2008.09.007" @default.
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