The H^1 -well-posedness for the inital-value problem of a semilinear SchrtSdinger equation with time-dependent coefficient is studied in R^N（N≥2）. Under Strichartz estimation and priori estimation for the solution, the relationship between the critical powers σ for the well-posedness and the order of the zeroes of the coefficient is obtained. And under some conditions,the H^1- local well-posedness and global well...
