On a Class of Nonlinear Integral Equations Arising in Transport Theory

Abstract

For a class of kernels $k(x,t)$, conditions are given for the existence and uniqueness of a solution in the unit ball of $L^1 (\mu )$ for the nonlinear integral equation \[u(x) = \psi (x) + u(x)\int {k(x,t)u(t)d\mu (t).} \] Equations of this type arise in the theories of radiative transfer, neutron transport and in the kinetic theory of gases.