About convergence of solutions of one-dimensional stochastic equations

In this paper, we consider a random process as a solution of stochastic differential equations with dependence of the coefficients on small parameter [Formula: see text] and we suppose that the drift coefficients of these equations are unbounded on the parameter [Formula: see text]. We consider more general requirements on the convergence of some functions of coefficients of stochastic equations to limit functions. Necessary and sufficient conditions for the weak convergence of solutions of such stochastic equations, if [Formula: see text] tends to zero to a some stochastic equations involving a local time of process, are obtained.