Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays

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  • FURUMOCHI Tetsuo
    DEPARTMENT OF MATHEMATICS SHIMANE UNIVERSITY
  • MURAKAMI Satoru
    DEPARTMENT OF APPLIED MATHEMATICS OKAYAMA UNIVERSITY OF SCIENCE
  • NAGABUCHI Yutaka
    DEPARTMENT OF SYSTEMS AND CONTROL ENGINEERING ANAN NATIONAL COLLEGE OF TECHNOLOGY DEPARTMENT OF APPLIED SCIENCE OKAYAMA UNIVERSITY OF SCIENCE

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We obtain a condition on the spectrum of the characteristic operator for the zero solution of Volterra difference equations on a Banach space to be exponen-tially asymptotically stable. Moreover, we apply some results obtained here to derive stability properties for some differential equations with piecewise continuous delays.

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