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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) $x(t)= \int_T G(t,s) r(s,x(s))ds$ 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 $\sigma$-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.

45G10Nonsingular nonlinear integral equations
47H30Particular nonlinear operators