# 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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