Well‐posedness for the massive nonlinear wave equation on asymptotically AdS spacetimes

In this paper, we prove some well‐posedness theorems for the nonlinear massive wave equation (with the mass satisfying the Breitenlohner‐Freedman bound) on asymptotically anti‐de Sitter spaces. The solution is constructed by contraction mapping method and also as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class.