aequationes mathematicae

, Volume 23, Issue 1, pp 197–203 | Cite as

On bounded time-dependent perturbations of operator cosine functions

  • Dieter Lutz
Research Papers


In this note it is shown that the Cauchy problem associated with the infinitesimal generatorA of a strongly continuous operator cosine function remains uniformly well-posed under bounded time-dependent perturbations ofA.

AMS (1980) subject classification

Primary 34G10, 39B70 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Fattorini, H. O.,Ordinary differential equations in linear topological spaces I–II. J. Differential Equations5 (1968), 72–105,6 (1969), 50–70.CrossRefGoogle Scholar
  2. [2]
    Nagy, B.,On cosine operator functions in Banach spaces. Acta. Sci. Math. (Szeged)36 (1974), 281–290.Google Scholar
  3. [3]
    Phillips, R. S.,Perturbation theory for semi-groups of linear operators. Trans. Amer. Math. Soc.74 (1953), 199–221.Google Scholar
  4. [4]
    Sova, M.,Cosine operator functions. Rozprawy Matematyczne, vol. XLIX. IMPAN, Warszawa, 1966.Google Scholar
  5. [5]
    Takenaka, T. andOkazawa, N.,A Phillips-Miyadera type perturbation theorem for cosine functions of operators. Tôhoku Math. J.30 (1978), 107–115.Google Scholar
  6. [6]
    Travis, C. C. andWebb, G. F.,Perturbation of strongly continuous cosine family generators. (preprint).Google Scholar

Copyright information

© Birkhäuser Verlag 1981

Authors and Affiliations

  • Dieter Lutz
    • 1
  1. 1.FB-6-MathematikUniversitat EssenEssen 1W. Germany

Personalised recommendations