Periodic Response Solutions to Multidimensional Nonlinear Schrödinger Equations with Unbounded Perturbation

This paper establishes the existence of periodic response solutions for multidimensional nonlinear Schrödinger equations (NLS) with unbounded perturbations. We adapt the Craig – Wayne – Bourgain (CWB) method to this context. The central point is that the core separation lemma remains valid for sufficiently weak unbounded perturbations, which allows the CWB method to be successfully applied. This work extends the applicability of the CWB method to problems with unbounded perturbations.