The Fokker–Planck–Kolmogorov equation with nonlinear terms of local and types

We study nonlinear Fokker–Planck–Kolmogorov equations and obtain sufficient conditions for existence and uniqueness of a nonnegative solution with a given value of the integral. We show convergence of solutions to the Cauchy problem to a solution of the stationary equation. An important difference from the known results is a very general form of nonlinearity, which enables one to consider simultaneously a local and nonlocal dependence of coefficients on solutions.