For the 3D focusing cubic nonlinear SchrSdinger equation, scattering of H1 solutions inside the （scale invariant） potential well was established by Holmer and Roudenko （radial case） and Duyckaerts et al. （general case） in 2008. In this paper, we extend this result to arbitrary space dimensions and focusing, mass-supercritical and energy-subcritical power nonlinearities, by adapting the method of Duyckaerts et al.
