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

• 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

Abstract

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.

Journal

• Japanese journal of mathematics. New series

  Japanese journal of mathematics. New series 30 (2), 387-412, 2004

  The Mathematical Society of Japan

Keywords

• Volterra difference equations
• stabilities
• piecewise continuous delays
• solution operator
• Z transform

Details

• CRID: 1390001205256687744
• NII Article ID: 10014334745
• NII Book ID: AA00690979
• DOI: 10.4099/math1924.30.387
• ISSN: 18613624
• ISSN: 02892316
• ISSN: http://id.crossref.org/issn/02892316
• MRID: 2111555
• NDL BIB ID: 7212178
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7212178
• Web Site: https://www.jstage.jst.go.jp/article/math1924/30/2/30_2_387/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed