  By using a classical truncated argument and introducing the local Wasserstein
distance, the global existence and uniqueness are proved for the distribution
dependent SDEs with local Lipschitz coefficients. Due to the measure
dependence, the conditions in the sense of pointwise for classical cases can be
simplified to the conditions in the sense of integral. On the basis of the
well-posedness, we prove the $r$-th moment exponential stability using the
measure dependent Lyapunov functions and the existence and uniqueness of
invariant probability measure is studied under the integrated strong
monotonicity condition. Finally, some examples are given to illustrate the
results in this paper.
