In this talk, we will discuss the existence of full dimensional tori for d-dimensional nonlinear Schrodinger equation with periodic boundary conditions. Here the radius of the invariant torus satisfies a slow decay. This result confirms a conjecture by Bourgain [J. Funct. Anal. 229 (2005), no. 1, 62-94]. This is a joint work with Xiaoqing Wu and Yuan Wu.
