Skip to main content
SpringerLink
Log in

On abstract Volterra equations in Banach spaces with completely positive kernels

  • Conference paper
  • First Online:
Infinite-Dimensional Systems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1076))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baillon, J.B., P. Clément: Ergodic Theorems for Non-Linear Volterra Equations in Hilbert Space, Nonlinear Anal. T.M.A., Vol. 5, No. 7, (1981), 789–801.

    Article  MATH  Google Scholar 

  2. Barbu, V.: Nonlinear Volterra Equations in Hilbert space, SIAM J. Math. Anal., 6 (1975), 728–741.

    Article  MathSciNet  MATH  Google Scholar 

  3. Clément, Ph.: On Abstract Volterra Equations with kernels having a positive resolvent, Israel J. Math. 36 (1980), 193–200.

    Article  MathSciNet  MATH  Google Scholar 

  4. Clément, Ph., J.A. Nohel: Abstract linear and nonlinear Volterra equations preserving positivity, SIAM J. Math. Anal. 10 (1979), 365–388.

    Article  MathSciNet  MATH  Google Scholar 

  5. Clément, Ph., J.A. Nohel: Asymptotic Behaviour of Solutions of Nonlinear Volterra equations with Completely Positive Kernels, SIAM J. Math. Anal. 12 (1981), 514–535.

    Article  MathSciNet  MATH  Google Scholar 

  6. Crandall, M.G., J.A. Nohel: An abstract functional differential equation and a related nonlinear Volterra equation, Israel J. Math. 29 (1978), 313–328.

    Article  MathSciNet  MATH  Google Scholar 

  7. Da Prato, G., P. Grisvard: Sommes d'opérateurs linéaires et équations differentielles opérationnelles, J. Math. pures et appl. 54 (1975), 305–388.

    MATH  Google Scholar 

  8. Friedman, A.: Monotonicity of solutions of Volterra integral equations in Banach spaces, Trans. Amer. Math. Soc. 138 (1969), 129–148.

    Article  MathSciNet  MATH  Google Scholar 

  9. Friedman, A., M. Shinbrot: Volterra integral equations in Banach space, Ibid., 126 (1967), 131–179.

    Article  MathSciNet  MATH  Google Scholar 

  10. Grimmer, R.C., R.K. Miller: Existence, uniqueness and continuity for integral equations in Banach space, J. Math. Anal. Appl. 57 (1977), 429–447.

    Article  MathSciNet  MATH  Google Scholar 

  11. Gripenberg, G.: On an abstract integral equation, SIAM J. Math. Anal. 10 (1979), 1017–1021.

    Article  MathSciNet  MATH  Google Scholar 

  12. Gripenberg, G.: On Volterra equations of the first kind, J. of Integral Eq. and Operator Th., 3/4 (1980), 473–488.

    Article  MathSciNet  MATH  Google Scholar 

  13. Londen, S.O.: On an integral equation in a Hilbert space, SIAM J. Math. Anal., 8 (1977), 950–970.

    Article  MathSciNet  MATH  Google Scholar 

  14. Mac Camy, R.C.: Nonlinear Volterra equations on a Hilbert space, J. Diff. Eq.,16 (1974), 373–393.

    Article  MathSciNet  Google Scholar 

  15. Mac Camy, R.C., R.L. Smith: Limits of Solutions of Nonlinear Volterra Equations, Appl. Analysis, 7 (1977), 19–27.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Hogeschool Delft, Onderafdeling der Wiskunde en Informatica, Julianalaan 132, 2628, BL Delft, The Netherlands

    Ph. Clément

Authors
  1. Ph. Clément
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Franz Kappel Wilhelm Schappacher

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Clément, P. (1984). On abstract Volterra equations in Banach spaces with completely positive kernels. In: Kappel, F., Schappacher, W. (eds) Infinite-Dimensional Systems. Lecture Notes in Mathematics, vol 1076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072763

Download citation

  • DOI: https://doi.org/10.1007/BFb0072763

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13376-6

  • Online ISBN: 978-3-540-38932-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation