Nonexistence results for semilinear elliptic equations on weighted graphs

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 nont...

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Bibliographic Details
Published inarXiv.org
Main Authors Dario Daniele Monticelli, Punzo, Fabio, Somaglia, Jacopo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.06.2023
Subjects
Elliptic functions
Graphs
Upper bounds
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Summary: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.
ISSN:2331-8422