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<p>This paper is concerned with the normalized solution of almost mass-critical nonlinear planar Schrödinger-Poisson system. The system has a logarithmic convolution, which leads to some difficulties in our research. We analyze concentration behavior of positive minimizers as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p \rightarrow 2^-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">→</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>. Moreover, we prove the uniqueness and orbital stability of positive minimizers for any <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p \in (2 - \sigma , 2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>-</mo> <mi>σ</mi> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Uniqueness and Stability for Almost Mass Critical Planar Schrödinger-Poisson System

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • Wei Long,
  • Changchang Yan

摘要

This paper is concerned with the normalized solution of almost mass-critical nonlinear planar Schrödinger-Poisson system. The system has a logarithmic convolution, which leads to some difficulties in our research. We analyze concentration behavior of positive minimizers as \(p \rightarrow 2^-\) p → 2 - . Moreover, we prove the uniqueness and orbital stability of positive minimizers for any \(p \in (2 - \sigma , 2)\) p ∈ ( 2 - σ , 2 ) .