Cybernetics and Systems Analysis

, Volume 30, Issue 6, pp 900–910 | Cite as

Existence of positive pseudo almost periodic solution for a class of functional equations arising in epidemic problems

  • E. Ait Dads
  • K. Ezzinbi
Systems Analysis

Keywords

Operating System Artificial Intelligence Periodic Solution System Theory Functional Equation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Ait Dads, O. Arino., and K. Ezzinbi, “Positive almost periodic solution for some nonlinear integral delay equation,” Submitted to J. Math. Anal. Appl.Google Scholar
  2. 2.
    E. Ait Dads, O. Arino, and K. Ezzinbi, “Positive Periodic Solution for some nonlinear integral delay equation” (preprint). — Marrakech, Morocco, 1994. — (Prepr. Marrakech, Univ. Cadi Ayyad, Dep. de Mathematique).Google Scholar
  3. 3.
    L. Amerio and G. Prouse, Almost-Periodic Functions and Functional Equations, New York, Van Nostrand (1971).Google Scholar
  4. 4.
    S. Busenberg and K. Cooke, “Periodic solutions to delay differential equations arising in some models of epidemiology,” Applied Nonlinear Analysis, Academic Press (1979), pp. 67–78.Google Scholar
  5. 5.
    K. Cooke, J. Kaplan, “A periodicity threshold theorem for epidemics and population growth,” Math. Biosci,31, 87–104 (1976).CrossRefMathSciNetGoogle Scholar
  6. 6.
    C. Corduneanu, Almost-Periodic Functions. 2nd Edn., New York, Chelsea (1989).Google Scholar
  7. 7.
    K. Deimling, Nonlinear Analysis, New York-Berlin, Springer-Verlag (1985).Google Scholar
  8. 8.
    K. Ezzinbi and M. A. Hachimi, “Existence of positive almost periodic solution through the use of the Hilbert projective metric in a class of functional equations,” Submitted to Nonlinear Analysis, T.M.A.Google Scholar
  9. 9.
    A. Fink, Almost-Periodic Differential Equations, Lect. Notes in Math., Vol. 377, New York-Berlin, Springer-Verlag (1974).Google Scholar
  10. 10.
    A. Fink and J. Gatika, “Positive almost periodic solution for some nonlinear integral delay equations,” J.D.E.,83, 166–178 (1990).Google Scholar
  11. 11.
    D. Guo and V. Lakshmikantham, “Positive solutions of nonlinear integral equations arising in infectious diseases,” J. Math. Anal. Appl.134, 1–8 (1988).CrossRefMathSciNetGoogle Scholar
  12. 12.
    J. Kaplan, M. Sorg, and J. Yorke, “Asymptotic behavior for epidemic equations,” Nonlinear Analysis, T.M.A.,5, 911–631 [sic] (1978).Google Scholar
  13. 13.
    R. Legget and L. Williams, “Nonzero solutions of nonlinear integral equations modeling infectious diseases,” SIAM J. Math. Anal.,33, No. 1, 112–121 (1983).Google Scholar
  14. 14.
    R. Nussbaum, “Hilbert's projective metric and iterated nonlinear maps,” Memoirs of the Amer. Math. Soc.,75, No. 391, 3–110 (1971).MathSciNetGoogle Scholar
  15. 15.
    H. L. Smith, “An abstract threshold theorem for one parameter families of positive non compact operator,” Funkcial. Ekvac.,24, 141–153 (1981).MATHMathSciNetGoogle Scholar
  16. 16.
    A. C. Thompson, “On certain contraction mappings in a partially ordered vector space,” Proc. Amer. Math. Soc.14, 438–443 (1963).MATHMathSciNetGoogle Scholar
  17. 17.
    R. Torrejon, “Positive almost periodic solution of a state-dependent delay nonlinear integral equation,” Nonlinear Analysis, T.M.A.,20, 1383–1416 (1993).MATHMathSciNetGoogle Scholar
  18. 18.
    S. Zaidman, “Solutions presque periodiques des equations differentielles abstraites,” Enseign. Math.,24, 87–110 (1978).MATHMathSciNetGoogle Scholar
  19. 19.
    C. Zhang, “Pseudo almost-periodic solutions of some differential equations,” J. Math. Anal. Appl.181, 62–76 (1994).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • E. Ait Dads
  • K. Ezzinbi

There are no affiliations available

Personalised recommendations