A quadratic integral equation

Roger D. Nussbaum

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1980)

  • Volume: 7, Issue: 3, page 375-480
  • ISSN: 0391-173X

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Nussbaum, Roger D.. "A quadratic integral equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.3 (1980): 375-480. <http://eudml.org/doc/83841>.

@article{Nussbaum1980,
author = {Nussbaum, Roger D.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {quadratic integral equation; existence theorems; continuity of solutions; positive solutions},
language = {eng},
number = {3},
pages = {375-480},
publisher = {Scuola normale superiore},
title = {A quadratic integral equation},
url = {http://eudml.org/doc/83841},
volume = {7},
year = {1980},
}

TY - JOUR
AU - Nussbaum, Roger D.
TI - A quadratic integral equation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1980
PB - Scuola normale superiore
VL - 7
IS - 3
SP - 375
EP - 480
LA - eng
KW - quadratic integral equation; existence theorems; continuity of solutions; positive solutions
UR - http://eudml.org/doc/83841
ER -

References

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  1. [1] L. Ahlfors, Complex Analysis, New York, McGraw-Hill Book Co., 1953. Zbl0052.07002MR510197
  2. [2] N. Baxter, Existence and uniqueness of positive solutions of a nonlinear integral equation, Ph. D. dissertation, Rutgers University, 1978. 
  3. [3] R.J. Baxter, Ornstein-Zernike relation for a disordered fluid, Austral. J. Phys., 21 (1968), pp. 563-569. 
  4. [4] L. Blum - J.S. Hoye, Solution of the Yukawa closure of the Ornstein-Zernike equation, J. Statist. Phys., 16 (1977), pp. 399-413. 
  5. [5] J. Cronin, Analytic functional mappings, Ann. of Math., 58 (1953), pp. 175-181. Zbl0050.34301MR57464
  6. [6] I.M. Gel'fand - D.A. Raikov - G.E. Silov, Commutative normed rings, Uspehi Mat. Nauk, 1 (1946), pp. 48-146 = Amer. Math. Soc. Transl., 5 (1957), pp. 165-220. Zbl0063.01567MR27130
  7. [7] M.G. Krein, Integral equations on a half-line with kernel depending upon the difference of the arguments, Uspehi Mat. Nauk, 13 (1958), pp. 3-120 = Amer. Math. Soc. Transl., Ser. 2, 22 (1962), pp. 163-288. Zbl0119.09601MR102721
  8. [8] B. Ja. Levin, Distribution of Zeros of Entire Functions, Translations of Math. Monographs, vol. 5, Amer. Math. Soc., Providence, Rhode Island, 1964. Zbl0152.06703MR156975
  9. [9] R. Paley - N. Wiener, Fourier Transforms in the Complex Domain, A.M.S. Colloquium Publications, vol. 15, New York, 1934. Zbl0011.01601
  10. [10] G. PimbleyJr., Positive solutions of a quadratic integral equation, Arch. Rational Mech. Anal., 24 (1967), pp. 107-127. Zbl0149.08103MR205010
  11. [11] P.H. Rabinowitz, A note on topological degree for holomorphic maps, Israel J. Math., 16 (1973), pp. 46-52. Zbl0278.32018MR346183
  12. [12] R. Ramalho, Existence and uniqueness theorems for a nonlinear integral equation, Math. Ann., 221 (1976), pp. 35-44. Zbl0303.45003MR402439
  13. [13] M. Wertheim, Analytic solutions of the Percus-Yevick equation, J. Mathematical Phys., 5 (1964), pp. 643-651. Zbl0128.22503MR161684
  14. [14] M. Wertheim, Exact solution of the mean spherical model for fluids of hard spheres with permanent electric dipole movements, J. Chem. Phys., 55 (1971), pp. 4291-4298. 
  15. [15] G. Whyburn, Topological Analysis, Princeton Univ. Press, Princeton, N.J., 1958. Zbl0080.15903
  16. [16] N. Baxter - R.D. Nussbaum, A nonlinear integral equation, in preparation. Zbl0489.45005
  17. [17] R.D. Nussbaum, A quadratic integral equation. II, submitted. Zbl0476.45009

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