Skip to main content

A semigroup proof of the Sharpe-Lotka theorem

  • Conference paper
  • First Online:

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

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bellman, R., K.L. Cooke: Differential-Difference Equations, Academic Press, New York 1963.

    MATH  Google Scholar 

  2. Browder, F.E.: On the spectral theory of elliptic operators, Math. Ann. 142 (1961), 22–130.

    Article  MathSciNet  MATH  Google Scholar 

  3. Derndinger, R.: Über das Spektrum positiver Generatoren, Math. Zeit. 172 (1980), 281–293.

    Article  MathSciNet  MATH  Google Scholar 

  4. Diekmann, O.: The stable size distribution: An example in structured population dynamics, Mathematisch Centrum Report TW 231, 1982, Amsterdam.

    Google Scholar 

  5. Dunford, N., J.T. Schwartz: Linear Operators, Part I: General Theory, Interscience, New York 1958.

    MATH  Google Scholar 

  6. Feller, W.: On the integral equation of renewal theory, Ann. Math. Stat. 12 (1941), 243–267.

    Article  MathSciNet  MATH  Google Scholar 

  7. Greiner, G.: Asymptotics in linear transport theory, Semesterbericht Funktionalanalysis Sommersemester, 1982, Tübingen.

    Google Scholar 

  8. Greiner, G., R. Nagel: On the stability of strongly continuous semigroups of positive operators on L2(μ), to appear.

    Google Scholar 

  9. Greiner, G., J. Voigt, M. Wolff: On the spectral bound of the generator of semigroups of positive operators, J. Operator Theory 5 (1981), 245–256.

    MathSciNet  MATH  Google Scholar 

  10. Groh, U., F. Neubrander: Stabilität startstetiger, positiver Operator-Halbgruppen auf C*-Algebren, Math. Ann. 256 (1981), 509–516.

    Article  MathSciNet  MATH  Google Scholar 

  11. Gurtin, M.E.: The Mathematical Theory of Age-Structured Populations, to appear.

    Google Scholar 

  12. Hoppensteadt, F.: Mathematical Theories of Populations: Demographics, Genetics and Epidemics, SIAM Regional Conference Series in Applied Mathematics, Philadelphia 1975.

    Google Scholar 

  13. Keyfitz, N.: Introduction to the Mathematics of Population, Addison-Wesley, Reading 1968.

    Google Scholar 

  14. Nussbaum, R.D.: The radius of the essential spectrum, Duke Math. J. 38 (1970), 473–478.

    Article  MathSciNet  MATH  Google Scholar 

  15. Oster, G.: Internal variables in population dynamics, Some Mathematical Questions in Biology VII, American Mathematical Society, Providence 1976.

    Google Scholar 

  16. Pollard, J.H.: Mathematical Models for the Growth of Human Populations, Cambridge University Press, Cambridge 1973.

    MATH  Google Scholar 

  17. Prüss, J.: Equilibrium solutions of age-specific population dynamics of several species, J. Math. Biol. 11 (1981), 65–84.

    Article  MathSciNet  MATH  Google Scholar 

  18. Prüss, J.: On the qualitative behavior of populations with age-specific interactions, Internat. J. Comput. Math. Appl. 9, No. 3 (1983), 327–339.

    Article  MATH  Google Scholar 

  19. Prüss, J.: Stability analysis for equilibria in age-specific population dynamics, to appear.

    Google Scholar 

  20. Royden, H.L.: Real Analysis, Second Edition, Macmillan, New York 1968.

    MATH  Google Scholar 

  21. Samuelson, P.A.: Resolving a historical confusion in population analysis, Human Biol. 48 (1976), 559–580.

    Google Scholar 

  22. Sharpe, F.R., A.J. Lotka: A problem in age distributions, Phil. Mag. 21 (1911), 435–438.

    Article  MATH  Google Scholar 

  23. Triggiani, R.: On the stabilizability problem in Banach space, J. Math. Anal. Appl. 52 (1975), 383–403.

    Article  MathSciNet  MATH  Google Scholar 

  24. Webb, G.F.: Theory of Nonlinear Age-Dependent Population Dynamics, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Franz Kappel Wilhelm Schappacher

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Webb, G.F. (1984). A semigroup proof of the Sharpe-Lotka theorem. In: Kappel, F., Schappacher, W. (eds) Infinite-Dimensional Systems. Lecture Notes in Mathematics, vol 1076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072780

Download citation

  • DOI: https://doi.org/10.1007/BFb0072780

  • 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