On α-times integrated C-semigroups and the abstract Cauchy problem
Kuo, Chung-Cheng ; Shaw, Sen-Yen
Studia Mathematica, Tome 141 (2000), p. 201-217 / Harvested from The Polish Digital Mathematics Library
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This paper is concerned with α-times integrated C-semigroups for α > 0 and the associated abstract Cauchy problem: u'(t)=Au(t)+tα-1Γ(α)x, t >0; u(0) = 0. We first investigate basic properties of an α-times integrated C-semigroup which may not be exponentially bounded. We then characterize the generator A of an exponentially bounded α-times integrated C-semigroup, either in terms of its Laplace transforms or in terms of existence of a unique solution of the above abstract Cauchy problem for every x in (λ-A)-1C(X).

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216798 
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     author = {Chung-Cheng Kuo and Sen-Yen Shaw},
     title = {On $\alpha$-times integrated C-semigroups and the abstract Cauchy problem},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {201-217},
     zbl = {0979.47028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p201bwm}
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Kuo, Chung-Cheng; Shaw, Sen-Yen. On α-times integrated C-semigroups and the abstract Cauchy problem. Studia Mathematica, Tome 141 (2000) pp. 201-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p201bwm/

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