On the solutions of a quadratic integral and an integral-differential equation (Q699311)

The integral equation \[ p(t)+ \int^\infty_0 p(s) p(s+ t) ds= {g(t)\over 2}\qquad (t> 0)\tag{1} \] and the integral-differential equation \[ p'(t)+ \mu p(t)+ \int^\infty_0 p(s) p(s+ t) ds= {g(t)\over 2},\tag{2} \] where \(\mu\in \mathbb{R}\), \(g\in L(\mathbb{R}_+)\cap L^2(\mathbb{R}_+)\), are considered. The author discusses the asymptotic behaviour, the estimation and the stability of the solutions for equations (1) and (2), and constructs the general solutions for the both equations.