SpringerLink
Log in

Asymptotic Representation of Solutions of Linear Autonomous Difference Equations

  • Conference paper
  • First Online:
Difference Equations, Discrete Dynamical Systems and Applications (ICDEA 2012)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 180))

Included in the following conference series:

  • 650 Accesses

Abstract

We establish an explicit asymptotic representation formula for solutions of linear autonomous difference equations with infinite delay. As an application, we investigate the limit of solutions of a certain delay difference equation in the critical case where the equation loses its asymptotic stability.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Levin, S.A., May, R.M.: A note on difference-delay equations. Theor. Popul. Biol. 9, 178–187 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  2. Matsunaga, H., Hara, T.: The asymptotic stability of a two-dimensional linear delay difference equation. Dyn. Contin. Discret. Impuls. Syst. 6, 465–473 (1999)

    MathSciNet  MATH  Google Scholar 

  3. Matsunaga, H., Murakami, S., Nagabuchi, Y., Nakano, Y.: Formal adjoint equations and asymptotic formula for solutions of Volterra difference equations with infinite delay. J. Differ. Equ. Appl. 18, 57–88 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Nagabuchi, Y.: Asymptotic periodic solutions for a two-dimensional linear delay difference system. Dyn. Contin. Discret. Impuls. Syst. Ser. A Math. Anal. 9, 187–200 (2002)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Osaka Prefecture University, Sakai, 599-8531, Japan

    Hideaki Matsunaga

Authors
  1. Hideaki Matsunaga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hideaki Matsunaga .

Editor information

Editors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola del Vallès, Barcelona, Spain

    Lluís Alsedà i Soler

  2. Department of Mathematics, University of Arizona, Tucson, Arizona, USA

    Jim M. Cushing

  3. Department of Mathematics, Trinity University, San Antonio, Texas, USA

    Saber Elaydi

  4. Faculty of Sciences, Department of Mathematics, University of Porto, Porto, Portugal

    Alberto A. Pinto

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Matsunaga, H. (2016). Asymptotic Representation of Solutions of Linear Autonomous Difference Equations. In: Alsedà i Soler, L., Cushing, J., Elaydi, S., Pinto, A. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2012. Springer Proceedings in Mathematics & Statistics, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52927-0_15

Download citation

Publish with us

Policies and ethics

Search

Navigation