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<p>In this paper, we investigate the existence of multiple nodal solutions for a class of planar Stein–Weiss problems involving a nonlinearity <i>f</i> with subcritical or critical growth in the sense of Trudinger–Moser. To this end, we combine a gluing technique with the Nehari manifold approach. We show that, for any positive integer <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k \in \mathbb {N}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </math></EquationSource> </InlineEquation>, the problem admits at least one radially symmetric ground state solution that changes sign exactly <i>k</i> times.</p>

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Multiple nodal solutions of planar Stein–Weiss equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月16日

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  • Eudes M. Barboza,
  • Eduardo Böer,
  • Olimpio H. Miyagaki,
  • Cláudia R. Santana

摘要

In this paper, we investigate the existence of multiple nodal solutions for a class of planar Stein–Weiss problems involving a nonlinearity f with subcritical or critical growth in the sense of Trudinger–Moser. To this end, we combine a gluing technique with the Nehari manifold approach. We show that, for any positive integer \(k \in \mathbb {N}\) k ∈ N , the problem admits at least one radially symmetric ground state solution that changes sign exactly k times.