Nonexistence results for semilinear elliptic equations on weighted graphs
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.
Authors
- Fabio Punzo (ORCID: https://orcid.org/0000-0001-8596-894X)
- Jacopo Somaglia (ORCID: https://orcid.org/0000-0003-0320-3025)
- Dario D. Monticelli (ORCID: https://orcid.org/0000-0002-0566-2850)
Institutions
- Politecnico di Milano (IT)
Publication Details
- Journal
- Mathematische Annalen
- Published
- 2025-10-20
- DOI
- https://doi.org/10.1007/s00208-025-03303-6
- Citations
- 5
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 18.64
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"