On solutions of a quadratic hammerstein integral equation on an unbounded interval

Abstract

In this paper we examine the solvability of a nonlinear quadratic Hammerstein integral equation. This equation is considered in the Banach space of real functions which are defined, bounded and continuous on the real half-line. Using the idea of measures of noncompactness with the classical Schauder fixed point theorem we show that the equation has solutions which vanish at infinity