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ArticleOriginal scientific text

Title

Hammerstein equations with an integral over a noncompact domain

Authors 1

Affiliations

  1. Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Abstract

The existence of solutions of Hammerstein equations in the space of bounded and continuous functions is proved. It is obtained by the Schauder fixed point theorem using a compactness theorem. The result is applied to Wiener-Hopf equations and to ODE's.

Keywords

ENG
Hammerstein operator, Wiener-Hopf equation

Bibliography

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  2. Yu. L. Daletskiĭ and M. G. Kreĭn, Stability of Solutions of Differential Equations in a Banach Space, Nauka, Moscow, 1970 (in Russian).
  3. J. Diestel and J. J. Uhl, Jr., Vector Measures, Amer. Math. Soc., Providence, R.I., 1977.
  4. A. Hammerstein, Nichtlineare Integralgleichungen nebst Anwendungen, Acta Math. 54 (1929), 117-176.
  5. B. Przeradzki, The existence of bounded solutions for differential equations in Hilbert spaces, Ann. Polon. Math. 56 (1992), 103-121.
  6. K. Yosida, Functional Analysis, Springer, Berlin, 1974.
Annales Polonici Mathematici
1998/69/1
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Pages:
49-60
Main language of publication
English
Received
1997-04-03
Accepted
1997-03-25
Published
1998
Exact and natural sciences