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<p>We consider multiple solutions to the nonlinear Schrödinger equation (NLS) with a partial confinement, which is physically relevant to dynamics of the Bose–Einstein condensate. Our study not only verifies the existence of positive ground state solutions and the nonexistence of least energy sign-changing solutions but also sheds light on the symmetry associated with these solutions.</p><p>A novel finding is the existence of saddle type nodal solutions with their nodal domains intersecting at the origin. Furthermore, we have developed some innovative techniques such as the method of moving planes and the Hopf lemma for nonlinear Schrödinger equations with partial confinement.</p>

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Multiple solutions to the nonlinear Schrödinger equation with a partial confinement

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Liying Shan,
  • Wei Shuai,
  • Leyun Wu

摘要

We consider multiple solutions to the nonlinear Schrödinger equation (NLS) with a partial confinement, which is physically relevant to dynamics of the Bose–Einstein condensate. Our study not only verifies the existence of positive ground state solutions and the nonexistence of least energy sign-changing solutions but also sheds light on the symmetry associated with these solutions.

A novel finding is the existence of saddle type nodal solutions with their nodal domains intersecting at the origin. Furthermore, we have developed some innovative techniques such as the method of moving planes and the Hopf lemma for nonlinear Schrödinger equations with partial confinement.