Existence and pathwise uniqueness of solutions for stochastic differential equations involving the local time at point zero

In this article, we aim to obtain the existence and pathwise uniqueness of the solution to the one-dimensional stochastic differential equations involving the local time (SDELT) at point zero. The existence and pathwise uniqueness theorem for class of SDELT is established under the drift coefficient satisfies a one-sided Lipschitz condition plus the superlinear condition.