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Spectral-Threshold and Normalized Solutions for Nonlinear Elliptic Equations on Finite Weighted Graphs
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DOI：10.1007/s00245-026-10389-0.png)
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Abstract
En 中文
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 Schr & ouml;dinger-type equation with prescribed mass and establish the existence and nonexistence of normalized solutions in every L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>2$$\end{document}-growth regime of the nonlinearity, without any restriction on the mass.
Keywords:
Finite weighted graphs
Discrete Laplacian
Nonlinear elliptic equations
Spectral-threshold solutions
Normalized solutions
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1.7
Papers:
106
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0
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