Normalized Solutions for Schrödinger Equations with Local Superlinear Nonlinearities

• Qin Xu ; Gui-Dong Li ^[1] ; Shengda Zeng ^[2]
  1. [1] Guizhou University

     Guizhou University

     China

     
  2. [2] Yulin Normal University

     Yulin Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we consider the following Schrödinger equation:

    where , , , and appears as a Lagrange multiplier. Assume that the nonlinear term f satisfies conditions only in a neighborhood of zero. For f has a subcritical growth, we prove the existence of the positive normalized solution for the equation with sufficiently small . For f has a supercritical growth, we derive the existence of the positive normalized solution for the equation with large enough. In addition, we also obtain infinitely many normalized solutions with sufficiently small for the subcritical case.