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Well-posedness of degenerate differential equations in Hölder continuous function spaces

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Abstract

Using known operator-valued Fourier multiplier results on vectorvalued Hölder continuous function spaces, we completely characterize the wellposedness of the degenerate differential equations (Mu)′(t) = Au(t) + f(t) for t ∈ ℝ in Hölder continuous function spaces C α(ℝ;X) by the boundedness of the M-resolvent of A, where A and M are closed operators on a Banach space X satisfying D(A) ⊂ D(M).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Shangquan Bu

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  1. Shangquan Bu
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Correspondence to Shangquan Bu.

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Bu, S. Well-posedness of degenerate differential equations in Hölder continuous function spaces. Front. Math. China 10, 239–248 (2015). https://doi.org/10.1007/s11464-014-0368-4

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  • DOI: https://doi.org/10.1007/s11464-014-0368-4

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