On the solutions of some nonlinear quadratic integral equations on an unbounded interval

In this paper, we study the existence of the solutions of a class of functional integral equations which contain a number of classical nonlinear integral equations as special cases. The investigations are placed in the Banach space of real functions defined, continuous on the real half-axis and vanishing at infinity. The method used in our considerations depends on suitable conjunction of the technique of measures of noncompactness with the classical Schauder fixed point theorem.  The results obtained in this paper extend and improve essentially some known results in the recent literature. Besides, three examples showing the generality and applicability of our results are presented.

Keywords:

Nonlinear Integral equation , Measure of noncompactness , Schauder fixed-point theorem