On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals
Aneta Sikorska-Nowak
Annales Polonici Mathematici, Tome 83 (2004), p. 257-267 / Harvested from The Polish Digital Mathematics Library
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We prove some existence theorems for nonlinear integral equations of the Urysohn type x(t)=φ(t)+λ∫0af(t,s,x(s))ds and Volterra type x(t)=φ(t)+∫0tf(t,s,x(s))ds, t∈Ia=[0,a], where f and φ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:280326 
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Aneta Sikorska-Nowak. On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals. Annales Polonici Mathematici, Tome 83 (2004) pp. 257-267. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-7/