Displaying similar documents to “On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem”

The Kneser property for the abstract Cauchy problem

Hernán R. Henríquez, Genaro Castillo G. (2003)

Annales Polonici Mathematici

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We establish existence of mild solutions for the semilinear first order functional abstract Cauchy problem and we prove that the set of mild solutions of this problem is connected in the space of continuous functions.

Decomposing and twisting bisectorial operators

Wolfgang Arendt, Alessandro Zamboni (2010)

Studia Mathematica

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Bisectorial operators play an important role since exactly these operators lead to a well-posed equation u'(t) = Au(t) on the entire line. The simplest example of a bisectorial operator A is obtained by taking the direct sum of an invertible generator of a bounded holomorphic semigroup and the negative of such an operator. Our main result shows that each bisectorial operator A is of this form, if we allow a more general notion of direct sum defined by an unbounded closed projection....