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<p>We study the zero mass nonlinear Schrödinger–Poisson system with doping profile, which appears in the semi-conductor theory. Due to the loss of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-term in the energy functional, methods performed in previous papers cannot be applied to our problem. A crucial point is that the functional involving the doping profile behaves as a lower order term of the Coulomb energy. We investigate the geometry of the energy functional carefully depending on <i>p</i>, and establish the existence of radial ground state solutions.</p>

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Nonlinear Schrödinger–Poisson system with doping profile: zero mass case

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Yu Su,
  • Tatsuya Watanabe

摘要

We study the zero mass nonlinear Schrödinger–Poisson system with doping profile, which appears in the semi-conductor theory. Due to the loss of \(L^2\) L 2 -term in the energy functional, methods performed in previous papers cannot be applied to our problem. A crucial point is that the functional involving the doping profile behaves as a lower order term of the Coulomb energy. We investigate the geometry of the energy functional carefully depending on p, and establish the existence of radial ground state solutions.