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<p>In this paper, we investigate the multiplicity results of normalized solutions for the nonlinear Dirac equation under <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-constraint, focusing on electron behavior in relativistic density functional theory. First, we establish the existence of multiple nonlinear eigenvalues under specific conditions on nonlinear potential. Additionally, we explore the nonrelativistic limit and show that solutions converge to those of a nonlinear Schrödinger equation as the speed of light approaches infinity. Our results encompass the mass-subcritical, mass-critical, and notably, the mass-supercritical cases.</p>

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Limit Behavior of Multiple Bound States of Nonlinear Dirac Equations

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Pan Chen,
  • Qi Guo,
  • Yuanyang Yu

摘要

In this paper, we investigate the multiplicity results of normalized solutions for the nonlinear Dirac equation under \(L^{2}\) L 2 -constraint, focusing on electron behavior in relativistic density functional theory. First, we establish the existence of multiple nonlinear eigenvalues under specific conditions on nonlinear potential. Additionally, we explore the nonrelativistic limit and show that solutions converge to those of a nonlinear Schrödinger equation as the speed of light approaches infinity. Our results encompass the mass-subcritical, mass-critical, and notably, the mass-supercritical cases.