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Nonexistence results for semilinear elliptic equations on weighted graphs

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arxiv 2306.03609 v1 pith:IZ3OGW6N submitted 2023-06-06 math.AP

Dario Daniele Monticelli , Fabio Punzo , Jacopo Somaglia This is my paper · ORCID
classification math.AP
keywords ellipticgraphssemilinearweightedadmitassumeballsbound
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonexistence results for the semilinear wave equation on graphs

    math.AP 2025-06 reject novelty 6.0 of 10

    On infinite weighted graphs, if the graph Laplacian of the distance grows slowly and suitable weighted volume growth holds, every very weak solution of the semilinear wave inequality is identically zero.

  2. On a semilinear parabolic equation with time-dependent source term on infinite graphs

    math.AP 2025-02 reject novelty 4.0 of 10

    For u_t = Δu + h(t)u^q on infinite graphs with λ1(G)>0, the paper claims blow-up for fast-growing h and global small data when ∫ h(t)e^{-λ1(q-1)t}dt is finite, but the general blow-up theorem is vitiated by a sign error.

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