On strong solution of a multidimensional SDE: extension of Yamada -- Watanabe's theorem

A new strong uniqueness result for a multidimensional SDE with a non-degenerate diffusion and partially irregular drift is established. It may be regarded as a combined variation on the themes of Yamada & Watanabe (1971), of Zvonkin (1974), and of the second author of the present paper (1980).