Pathwise uniqueness for solutions of systems of stochastic differential equations

A general theorem which obtains pathwise uniqueness for solutions of systems of Ito stochastic differential equations is given. It is shown that this theorem contains as special cases basic criteria which generalize Ito's result in which the coefficients satisfy Lipschitz conditions in the second variable. Also some new results which assume t-dependent modulus of continuity conditions on the coefficients are given as corollaries. The main result is established by means of Lyapunov type functions and comparison principle techniques.