On a functional differential equation arising in the theory of the distribution of wealth (Q1059771)

The paper under review deals with the functional differential equation \((i)\quad p_ t(x,t)+(\beta +n\gamma)p(x,t)+\beta xp_ x(x,t)=\gamma n^ 2p(nx,t),\) \(x,t\in (0,+\infty)\), arising in the theory of the distribution of wealth. The author studies properties of solutions of (i) of the type \(p(x,t)=p(t)x^{-c},\) where \(c>1\), and multiplicative solutions \(\psi (x,t)=u(x)v(t)\). The proof uses an explicit expression of solutions of an initial problem for (i).