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Frontiers of Mathematics in China

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Front. Math. China    2015, Vol. 10 Issue (2) : 239-248    https://doi.org/10.1007/s11464-014-0368-4
RESEARCH ARTICLE
Well-posedness of degenerate differential equations in H?lder continuous function spaces
Shangquan BU()
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
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Abstract

Using known operator-valued Fourier multiplier results on vectorvalued H?lder continuous function spaces, we completely characterize the wellposedness of the degenerate differential equations (Mu)'(t)=Au(t)+f(t) for t∈R in H?lder continuous function spaces Ca(R;X)<?Pub Caret?> 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).
Keywords Well-posedness      degenerate differential equation      C ˙α-multiplier')" href="#">C ˙α-multiplier      H?older continuous function space     
Corresponding Author(s): Shangquan BU   
Issue Date: 12 February 2015
 Cite this article:   
Shangquan BU. Well-posedness of degenerate differential equations in H?lder continuous function spaces[J]. Front. Math. China, 2015, 10(2): 239-248.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0368-4
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I2/239
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https://doi.org/10.1017/S0013091513000606
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