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arXiv · 2306.03609

Nonexistence results for semilinear elliptic equations on weighted graphs

Dario Daniele Monticelli·Fabio Punzo·Jacopo Somaglia
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Abstract

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.

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Dario Daniele Monticelli, Fabio Punzo, Jacopo Somaglia. 2023-06-06. Nonexistence results for semilinear elliptic equations on weighted graphs. https://arxiv.org/abs/2306.03609

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