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<p>In this paper, we study nonlinear elliptic equations on finite weighted graphs from two complementary perspectives. First, we investigate a discrete analogue of the classical Yamabe-type problem, focusing on the existence and nonexistence of spectral-threshold solutions. Secondly, we consider a Schrödinger-type equation with prescribed mass and establish the existence and nonexistence of normalized solutions in every <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-growth regime of the nonlinearity, without any restriction on the mass.</p>

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Spectral-Threshold and Normalized Solutions for Nonlinear Elliptic Equations on Finite Weighted Graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月9日

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  • Renan J. S. Isneri,
  • Chao Ji,
  • Olimpio H. Miyagaki

摘要

In this paper, we study nonlinear elliptic equations on finite weighted graphs from two complementary perspectives. First, we investigate a discrete analogue of the classical Yamabe-type problem, focusing on the existence and nonexistence of spectral-threshold solutions. Secondly, we consider a Schrödinger-type equation with prescribed mass and establish the existence and nonexistence of normalized solutions in every \(L^2\) L 2 -growth regime of the nonlinearity, without any restriction on the mass.