Hammerstein equations with an integral over a noncompact domain

• Autorzy: Robert Stańczy
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hammerstein operator; Wiener-Hopf equation

Kategorie tematyczne

• 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytski{\u\i}, Uryson, etc.)
• 45G10: Other nonlinear integral equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 69
• Numer: 1
• Strony: 49-60

Daty

wydano

1998

poprawiono

1997-03-25

otrzymano

1997-04-03

poprawiono

1997-11-17

Twórcy

autor

Robert Stańczy

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

Bibliografia

• [1] J. Banaś, Measures of noncompactness in the space of continuous tempered functions, Demonstratio Math. 14 (1981), 127-133.
• [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.