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May 14, 2026Zeitschrift für angewandte Mathematik und PhysikOpen Access

Solutions with prescribed mass for critical Schrödinger–Poisson systems concentrating at a potential well

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Authors

QGQi GaoXHXiaoming HeVRVicenţiu D. Rădulescu

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Overview

Demonstrates the existence of normalized solutions in critical Schrödinger–Poisson systems, suggesting implications for semiclassical states.

Key Points

  • The aim is to explore the existence and multiplicity of normalized solutions to the Schrödinger–Poisson system with prescribed mass.
  • Analyzed the system using truncation techniques and appropriate estimates.
  • Employed Ljusternik-Schnirelmann theory to relate solutions' existence to the topology of the potential's minimum.
  • Focused on solutions in the whole space \( \mathbb{R}^3 \) for small values of the parameter \( \varepsilon > 0 \).
  • Normalized solutions exist for sufficiently small \( \varepsilon > 0 \).
  • The number of positive solutions is linked to the topology of the set where the potential \( V \) attains its minimum.

Cite This Study

Gao et al. (2026) studied this question.

synapsesocial.com/papers/6a05684ea550a87e60a20c96https://doi.org/10.1007/s00033-026-02810-z
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