Existence and uniqueness of solutions for stochastic differential equations with locally one-sided Lipschitz condition

This paper investigates stochastic differential equations (SDEs) with locally one-sided Lipschitz coefficients. Apart from the local one-sided Lipschitz condition, a more general condition is introduced to replace the monotone condition. Then, in terms of the Euler’s polygonal line method, the existence and uniqueness of solutions for SDEs is established. In the meanwhile, the $p$th moment boundedness of solutions is also provided.