Existence and Mass Collapse of Standing Waves for Equation with General Potential and Nonlinearities

Yu Su ^[1] ; Hongxia Shi ^[3] ; Jie Yang ^[2]
1. [1] Anhui University of Science and Technology
  
  Anhui University of Science and Technology
  
  China
2. [2] Huaihua University
  
  Huaihua University
  
  China
3. [3] Hunan First Normal University
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
Idioma: inglés
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Resumen
- We are concerned with the existence and mass collapse of standing waves with prescribed mass for the Schrödinger equation with general potential and nonlinearities. For local nonlinearities, this equation arises in the theory of Bose–Einstein condensates. For nonlocal nonlinearities, this equation is the Choquard euqation, which appears in the quantum theory of a polaron at rest. We used a unified approach (local minizing method) to study the existence of standing waves for the local, nonlocal and dipolar type cases. And then we established the mass collapse result.