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

Nonlinear Fokker–Planck–Kolmogorov equations are investigated. Sufficient conditions are obtained for the existence and uniqueness of a nonnegative solution with a prescribed value of the integral. Convergence of solutions for the Cauchy problem to a solution of the stationary equation is shown. An important distinction from the known results is a very general form of the nonlinearity, which makes it possible to consider simultaneously a local and nonlocal dependence of coefficients on solutions.