Existence theorem for the Hammerstein integral equation
Mieczysław Cichoń ; Ireneusz Kubiaczyk
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 16 (1996), p. 171-177 / Harvested from The Polish Digital Mathematics Library
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In this paper we prove an existence theorem for the Hammerstein integral equation x(t)=p(t)+λ∫IK(t,s)f(s,x(s))ds, where the integral is taken in the sense of Pettis. In this theorem continuity assumptions for f are replaced by weak sequential continuity and the compactness condition is expressed in terms of the measures of weak noncompactness. Our equation is considered in general Banach spaces.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:275952 
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     year = {1996},
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     zbl = {0911.45009},
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Mieczysław Cichoń; Ireneusz Kubiaczyk. Existence theorem for the Hammerstein integral equation. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 16 (1996) pp. 171-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div16i2n6bwm/

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