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On α-times integrated C-semigroups and the abstract Cauchy problem

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Kuo C.-C., Shaw S.-Y.

Studia Mathematica

2000

tom 142

nr 3

201-217

This paper is concerned with α-times integrated C-semigroups for α > 0 and the associated abstract Cauchy problem: $u'(t) = Au(t) + \frac{t^{α-1}}{Γ(α)}x$, 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 $(λ-A)^{-1}C(X)$.

Ograniczanie wyników

1 Studia Mathematica

1 Kuo C.-C.

1 Shaw S.-Y.

1 2000

Wyniki wyszukiwania

On α-times integrated C-semigroups and the abstract Cauchy problem