  In this paper we study second order stochastic differential equations with
measurable and density-distribution dependent coefficients. Through
establishing a maximum principle for kinetic Fokker-Planck-Kolmogorov equations
with distribution-valued inhomogeneous term, we show the existence of weak
solutions under mild assumptions. Moreover, by using the H\"older regularity
estimate obtained recently in \cite{GIMV19}, we also show the well-posedness of
generalized martingale problems when diffusion coefficients only depend on the
position variable (not necessarily continuous). Even in the non
density-distribution dependent case, it seems that this is the first result
about the well-posedness of SDEs with measurable diffusion coefficients.
