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Hammerstein equations with an integral over a noncompact domain. (English) Zbl 0919.45004
Applying the Schauder fixed point principle a few theorems on the existence of continuous solutions of the Hammerstein integral equation (1) x(t)= T G(t,s)r(s,x(s))ds are established. The author investigates a very general case assuming that T is a noncompact domain (more precisely: T is a metric locally compact space countable at infinity and equipped with a measure on σ-algebra of Borel subsets of T) and the values of the functions involved are situated in a Banach space X. Applications to a nonlinear Wiener-Hopf integral equation are also derived.
MSC:
45G10Nonsingular nonlinear integral equations
47H30Particular nonlinear operators