Solving a non-linear integral equation

Question

Is there any way to solve an integral equation of this type,

$s(1-b)f(s)=\int^s_{sb}f(x)f(x-sb)dx$

Any help would be highly appreciated.

Answer 1

You can solve this type of nonlinear equation by the Kantrivich method, it is a numerical method, so you start by linearizing the equation and approximate the linear equation obtained by the Nythrom method.