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On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval

Olszowy L.

Commentationes Mathematicae

2008

Vol. 48, [Z] 1

103-112

We show that [formula] is a measure of noncompactness defined on some subsets of the space C(R+) = {x : R+ !R, x continuous} furnished with the distance defined by the family of seminorms |x|n. Moreover, using a technique associated with the measures of noncompactness, we prove the existence of solutions of a quadratic Urysohn integral equation on an unbounded interval. This measure allows to obtain theorems on the existence of solutions of a integral equations on an unbounded interval under a weaker assumptions then the assumptions of theorems obtained by applying two-component measures of noncompactness.