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Annali di Matematica Pura ed Applicata

, Volume 80, Issue 1, pp 135–152 | Cite as

Existence, uniqueness and continuity of solutions of integral equations

  • Richard K. Miller
  • George R. Sell
Article

Keywords

Integral Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    L. Cesari,Asymptotic behavior and stability problems in ordinary differential equations, Second edition, Academic Press, New York, (1963)zbMATHGoogle Scholar
  2. [2]
    C. Corduneanu,Problèmes globaux dans la théorie des équations intégrales da Volterra, Ann. Mat. Pura Appl. (4),67 (1965), pp. 349–363.zbMATHMathSciNetGoogle Scholar
  3. [3]
    J. Gronin,Fixed points and topological degree in nonlinear analysis, Amer. Math. Soc., Providence, R. I, (1964).Google Scholar
  4. [4]
    E. Kamke,Zur Theorie der Systeme gervöhnlicher Differentialgleichungen II, Acta. Math.58 (1932), pp. 57–85.zbMATHMathSciNetGoogle Scholar
  5. [5]
    H. Kneser,Über die Lösungen eines Systems gewöhnlicher Differentialgleichungen das der Lipschitzschen Bedingung nicht genügts, Sitzber. Preuss. Akad. Wiss. Phys. Math. Kl. (1923), pp. 171–174.Google Scholar
  6. [6]
    M. A. Krasnosel'skii,Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, New York, (1964).Google Scholar
  7. [7]
    L. A. Ladyzenskii,Conditions for the complete continuity of P. S. Uryson's integral operator in the space of continuous functions, Dokl. Akad. Nauk SSSR97 (1954). pp. 1105–1108.MathSciNetGoogle Scholar
  8. [8]
    J. A. Nohel,Some problems in nonlinear Volterra integral equations, Bull. Amer. Mat. Soc.68 (1962), pp. 323–329.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Z. Opial,Sur la dépendance des solutions d'un système d'équations différentielles de leurs seconds membres. Applications aux systèmes presque autonomes, Ann. Polon. Math.8 (1960), pp. 75–89.zbMATHMathSciNetGoogle Scholar
  10. [10]
    M. Reichert,Eindeutigkeits-und Interationsfragen bei Volterra-Hammersteinschen Integralgleichungen, J. Reine Angew. Math.,220 (1965), pp. 74–87.zbMATHMathSciNetGoogle Scholar
  11. [11]
    T. Sato,Sur l'équation intégrale non linéaire de Volterra, Compositio Math.,11 (1953), pp. 271–290.zbMATHMathSciNetGoogle Scholar
  12. [12]
    G. R. Sell,On the fundamental theory of ordinary differential equations, J. Diff. Equations,1 (1965), pp. 370–392.CrossRefzbMATHMathSciNetGoogle Scholar
  13. [13]
    G. R. Sell,Nonautonomous differential equations and topological dynamics I. The basic theory, Trans. Amer. Math. Soc.127 (1967), pp. 241–262.CrossRefzbMATHMathSciNetGoogle Scholar
  14. [14]
    D. Willett,Nonlinear vector integral equations as contraction mappings, Arch. Rational Mech. Anal.,15 (1964), pp. 79–86.CrossRefzbMATHMathSciNetGoogle Scholar
  15. [15]
    J. J. Levin andJ. A. Nohel,On a system of integrodifferential equations occurring in reactor dynamics, II, Archive Rat. Mech. Anal.,11 (1962), pp. 210–243.CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1968

Authors and Affiliations

  • Richard K. Miller
    • 1
  • George R. Sell
    • 2
  1. 1.Division of Applied Mathematics Brown University Providence
  2. 2.School of Mathematics University of Minnesota MinneapolisMinnesota and University of Southern CaliforniaLos Angeles

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