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<p>In this paper, we study the existence of solutions to the stationary nonlinear Choquard equation with an Aharonov–Bohm magnetic potential, which generates a magnetic field corresponding to a thin and infinitely long solenoid. By employing a minimizing argument on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-sphere, the multiplicity of normalized solutions is established. Furthermore, we characterize certain symmetry properties of these solutions.</p>

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Multiple normalized solutions for the nonlinear Choquard equation in the Aharonov–Bohm magnetic field

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Baihong Li,
  • Yuanhong Wei

摘要

In this paper, we study the existence of solutions to the stationary nonlinear Choquard equation with an Aharonov–Bohm magnetic potential, which generates a magnetic field corresponding to a thin and infinitely long solenoid. By employing a minimizing argument on the \(L^2\) L 2 -sphere, the multiplicity of normalized solutions is established. Furthermore, we characterize certain symmetry properties of these solutions.