Abstract: The existence of generalized solution to the initial value problem iu_t+△u+k/(x_N)u_XN+q(x)u+|u|^p-1u=0 on R^N is studied, By Galerkin method, we prove that the solution always exists for every initial value in H¹(R^N; k) if 1 < p < (N+k)/(N+k-2), N ≥ 2. Finally, we prove orbital stability of standing waves for nonlinear singular Schrödinger equation.