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<p>This paper establishes the existence of periodic response solutions for multi-dimensional 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.</p>

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Periodic Response Solutions to Multidimensional Nonlinear Schrödinger Equations with Unbounded Perturbation

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Zuhong You,
  • Xiaoping Yuan

摘要

This paper establishes the existence of periodic response solutions for multi-dimensional 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.