Integrable solutions of Hammerstein and Urysohn integral equations. (English) Zbl 0666.45008

The author proves and discusses the existence of monotone \(L^ 1\)- solutions to Hammerstein and Urysohn integral equations by means of a fixed-point principle of G. Emmanuele [Bull. Math. Soc. Sci. Math. R. S. Roum. 25, 353-358 (1981; Zbl 0482.47027)], which in turn builds on the measure of weak noncompactness introduced by F. S. De Blasio [ibid. 21, 259-262 (1977; Zbl 0365.46015)].
Reviewer: J.Appell


45G10 Other nonlinear integral equations
47J05 Equations involving nonlinear operators (general)