On bounded time-dependent perturbations of operator cosine functions

DOI10.1007/BF02188032zbMath0512.34047MaRDI QIDQ1839351

Dieter Lutz

Publication date: 1981

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/136910

zbMATH Keywords

cosine operator functionsabstract Cauchy problems

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Functional equations for functions with more general domains and/or ranges (39B52) Linear differential equations in abstract spaces (34G10) Algebras of operators on Banach spaces and other topological linear spaces (47L10)

Related Items (9)

Existence of solutions of abstract non-autonomous second order integro-differential equations ⋮ Existence of solutions of the nonautonomous abstract Cauchy problem of second order ⋮ On solutions of the second generalization of d'Alembert's functional equation on a restricted domain ⋮ Perturbation properties of fractional strongly continuous cosine and sine family operators ⋮ Existence of solutions of non-autonomous second order functional differential equations with infinite delay ⋮ Unnamed Item ⋮ Bounded perturbation for evolution equations with a parameter \& application to population dynamics ⋮ Semigroups of operators, cosine operator functions, and linear differential equations ⋮ Perturbation theory for fractional evolution equations in a Banach space

Cites Work

• Ordinary differential equations in linear topological spaces. I
• Perturbation Theory for Semi-Groups of Linear Operators
• A Phillips-Miyadera type perturbation theorem for cosine functions of operators
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