Properties of solutions of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion

Properties of solutions of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion are studied in the paper. Conditions on the coefficients of an equation are obtained ensuring that a solution does not vanish over a finite time interval in the case of the diffusion $\sigma(t)\sqrt{x}$. We prove a limit theorem that solutions continuously depend on the parameter $n$ in the space $L_1(\mathsf{P})$ for a sequence of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion.