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