Hammerstein equations with an integral over a noncompact domain
Annales Polonici Mathematici (1998)
- Volume: 69, Issue: 1, page 49-60
- ISSN: 0066-2216
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topRobert Stańczy. "Hammerstein equations with an integral over a noncompact domain." Annales Polonici Mathematici 69.1 (1998): 49-60. <http://eudml.org/doc/270625>.
@article{RobertStańczy1998,
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.},
author = {Robert Stańczy},
journal = {Annales Polonici Mathematici},
keywords = {Hammerstein operator; Wiener-Hopf equation; Schauder fixed point principle; existence; continuous solutions; Hammerstein integral equation; noncompact domain; nonlinear Wiener-Hopf integral equation},
language = {eng},
number = {1},
pages = {49-60},
title = {Hammerstein equations with an integral over a noncompact domain},
url = {http://eudml.org/doc/270625},
volume = {69},
year = {1998},
}
TY - JOUR
AU - Robert Stańczy
TI - Hammerstein equations with an integral over a noncompact domain
JO - Annales Polonici Mathematici
PY - 1998
VL - 69
IS - 1
SP - 49
EP - 60
AB - 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.
LA - eng
KW - Hammerstein operator; Wiener-Hopf equation; Schauder fixed point principle; existence; continuous solutions; Hammerstein integral equation; noncompact domain; nonlinear Wiener-Hopf integral equation
UR - http://eudml.org/doc/270625
ER -
References
top- [1] J. Banaś, Measures of noncompactness in the space of continuous tempered functions, Demonstratio Math. 14 (1981), 127-133. Zbl0462.47035
- [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. Zbl0805.47041
- [6] K. Yosida, Functional Analysis, Springer, Berlin, 1974.
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