  We study a nonlinear branching diffusion process in the sense of McKean,
i.e., where particles are subjected to a mean-field interaction. We consider
first a strong formulation of the problem and we provide an existence and
uniqueness result by using contraction arguments. Then we consider the notion
of weak solution and its equivalent martingale problem formulation. In this
setting, we provide a general weak existence result, as well as a propagation
of chaos property, i.e., the McKean-Vlasov branching diffusion is the limit of
a large population branching process with mean-field interaction when the
population size grows to infinity.
