| Abstract: |
| We study semilinear elliptic inequalities on infinite weighted graphs. Given a distance on the graph, assuming an upper bound on its Laplacian, and a growth condition on a suitable weighted volume of balls, we show that the following semilinear elliptic inequality
\[\Delta u+v(x)u \leq 0,\]
where $v$ is a positive potential, admits no nonnegative solution. The parabolic case is also discussed. This is a joint work with Dario Monticelli and Fabio Punzo. |
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