The paper presents some results on the existence of solutions vanishing at infinity of a quadratic Hammerstein integral equation of Stieltjes type. We investigate solutions of the mentioned integral equation which are defined, continuous and bounded on the real half-axis ℝ + . The main tools used in our investigations are the technique of measures of noncompactness and a fixed point theorem of Darbo type. Moreover, we introduce the concept of the variation of a function on an unbounded interval and the integral of Stieltjes type defined on such an interval. Our result will be illustrated by an appropriate example.
Banas et al. (Wed,) studied this question.