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<p>We study semilinear elliptic inequalities with a potential on infinite graphs. Given a distance on the graph, we assume an upper bound on its Laplacian, and a growth condition on a suitable weighted volume of balls. Under such hypotheses, we prove that the problem does not admit any nonnegative nontrivial solution. We also show that our conditions are optimal.</p>

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Nonexistence results for semilinear elliptic equations on weighted graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月20日

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  • Dario D. Monticelli,
  • Fabio Punzo,
  • Jacopo Somaglia

摘要

We study semilinear elliptic inequalities with a potential on infinite graphs. Given a distance on the graph, we assume an upper bound on its Laplacian, and a growth condition on a suitable weighted volume of balls. Under such hypotheses, we prove that the problem does not admit any nonnegative nontrivial solution. We also show that our conditions are optimal.