Applying the Schauder fixed point principle a few theorems on the existence of continuous solutions of the Hammerstein integral equation (1)
are established. The author investigates a very general case assuming that
is a noncompact domain (more precisely:
is a metric locally compact space countable at infinity and equipped with a measure on
-algebra of Borel subsets of
) and the values of the functions involved are situated in a Banach space
. Applications to a nonlinear Wiener-Hopf integral equation are also derived.