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Perturbation and comparison of cosine operator functions

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Abstract

LetA be a closed linear operator such that the abstract Cauchy problemu″(t)=Au(t), t∈R; u(0)=x, u′(0)=y, is well-posed. We present some multiplicative perturbation theorems which give conditions on an operatorC so that the abstract Cauchy problems for differential equationsu″(t)=ACu(t) andu″(t)=CAu(t) also are well-posed. Some new or known additive perturbation theorems and mixed-type perturbation theorems are deduced as corollaries. Applications to characterization of the infinitesimal comparison of two cosine operator functions are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, National Central University, Chung-Li, Taiwan, Republic of China

    S. Piskarev & S. -Y. Shaw

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  1. S. Piskarev
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  2. S. -Y. Shaw
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Communicated by J. Goldstein

Research supported in part by the National Science Council of Taiwan.

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Piskarev, S., Shaw, S.Y. Perturbation and comparison of cosine operator functions. Semigroup Forum 51, 225–246 (1995). https://doi.org/10.1007/BF02573631

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  • DOI: https://doi.org/10.1007/BF02573631

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