On the Solutions of a Quadratic Integral and an Integral-Differential Equation

Abstract

An integral equation and a related integral-differential equation of first order over ${\mathbb{R}}_{+}$ with a quadratic integral term representing the so-called autocorrelation of the unknown function is dealt with. For both equations the general solution is constructed and estimated in the $L^2$-norm. Further, the asymptotic behaviour and the stability of the solution are investigated.