Work

Nonexistence results for semilinear elliptic equations on weighted graphs

Year: 2025

Type: article

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.

Source: Mathematische Annalen

DOI: 10.1007/s00208-025-03303-6

Authors: Dario D. Monticelli, Fabio Punzo, Jacopo Somaglia

Institution: Politecnico di Milano

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Politecnico di Milano