Bulletin of the American Mathematical Society

Monotone operators and nonlinear integral equations of Hammerstein type

Felix E. Browder and Chaitan P. Gupta

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 75, Number 6 (1969), 1347-1353.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183530927

Mathematical Reviews number (MathSciNet)
MR0250141

Zentralblatt MATH identifier
0193.11204

Citation

Browder, Felix E.; Gupta, Chaitan P. Monotone operators and nonlinear integral equations of Hammerstein type. Bull. Amer. Math. Soc. 75 (1969), no. 6, 1347--1353. https://projecteuclid.org/euclid.bams/1183530927


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References

  • 1. H. Amann, Über die Existenz una iterative Berechnung einer Lösung der Hammersteinschen Gleichung, Aequations Math. 1 (1968), 242-266.
  • 2. H. Amann, Ein Existenz und Eindeutigkeitssatz für die Hammersteinsche Gleichung in Banachraumen, Math. Z. (to appear).
  • 3. H. Brézis, Equations et inequations non-linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble) 18 (1968), 115-176.
  • 4. F. E. Browder, The solvability of non-linear functional equations, Duke Math. J. 30 (1963), 557-566.
  • 5. F. E. Browder, Nonlinear elliptic boundary value problems, Bull. Amer. Math. Soc. 69 (1963), 862-874.
  • 6. F. E. Browder, "Nonlinear operators and nonlinear equations of evolution in Banach spaces" in Non-linear functional analysis, Proc. Amer. Math. Soc. Sympos. (to appear).
  • 7. C. L. Dolph, Non-linear integral equations of Hammerstein type, Trans. Amer. Math. Soc. 66 (1949), 289-307.
  • 8. C. Dolph and G. J. Minty, On nonlinear integral equations of the Hammerstein type. Nonlinear integral equations, edited by P. M. Anselone, Univ. of Wisconsin Press, Madison, Wis., 1964, pp. 99-154.
  • 9. D. G. de Figueiredo and C. P. Gupta, Solvability of nonlinear integral equations of Hammerstein type (to appear).
  • 10. M. Golomb, On the theory of nonlinear integral equations, integral systems and general functional equations, Math. Z. 39 (1935), 45-75.
  • 11. A. Hammerstein, Nichtlineare Integralgleichungen nebst Anwendungen, Acta Math. 54 (1930), 117-176.
  • 12. R. Iglisch, Existenz und Eindeutigkeit Satze bei nichtlineare Integralgleichungen, Math. Ann. 108 (1933), 161-189.
  • 13. 1.1. Kolodner, Equations of Hammerstein type in Hubert space, J, Math Mech. 13 (1964), 701-750.
  • 14. J. Kolomy, Applications of some existence theorems for the solutions of Hammerstein integral equations, Comment. Math. Univ. Carolinae 7 (1966), 461-478.
  • 15. J. Kolomy, The solvability of nonlinear integral equations, Comment. Math. Univ. Carolinae 8 (1967), 273-289.
  • 16. M. A. Krasnosel'skiĭ, Topological methods in the theory of non-linear integral equations, GITTL, Moscow, 1956; English transl., Macmillan, New York, 1964.
  • 17. G. J. Minty, On a "monotonicity" method for the solution of nonlinear equations in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1038-1041.
  • 18. E. R. Rothe, Weak topology and nonlinear integral equations, Trans. Amer. Math. Soc. 66 (1949), 75-92.
  • 19. M. Vainberg, Variational methods for the study of non-linear operators, GITTL, Moscow, 1956; English transl., Holden-Day, San Francisco, Calif., 1964.
  • 20. M. Vainberg, New theorems for nonlinear operators and equations, Moskov. Oblast. Ped. Inst. Učen Zap. 77 (1959), 131-143. (Russian)
  • 21. M. Vainberg, Nonlinear problems for potential and monotone operators, Dokl. Akad. Nauk SSSR 183 (1968), 747-749= Soviet Math. Dokl. 9 (1968), 1427-1430.