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<p>In this paper, we are concerned with the equivalent minimization problems for the ground states of Schrödinger–Poisson–Slater equations, which are described by minimizing the corresponding energy functionals in several manifolds with constrained conditions. To overcome the difficulty from the lack of compactness, we construct a Palais–Smale–Pohozaev identity from a bounded Palais–Smale sequence, and consequently we are able to calculate the exact value of Lagrange multipliers. The classical variational principle and the Coulomb–Sobolev inequality come into play here.</p>

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Equivalent Conditions for Ground State Solutions to the Schrödinger–Poisson–Slater Equations

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Chunyu Lei,
  • Zhisu Liu,
  • Binlin Zhang

摘要

In this paper, we are concerned with the equivalent minimization problems for the ground states of Schrödinger–Poisson–Slater equations, which are described by minimizing the corresponding energy functionals in several manifolds with constrained conditions. To overcome the difficulty from the lack of compactness, we construct a Palais–Smale–Pohozaev identity from a bounded Palais–Smale sequence, and consequently we are able to calculate the exact value of Lagrange multipliers. The classical variational principle and the Coulomb–Sobolev inequality come into play here.