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Uniqueness for the Schrödinger Equation on Graphs with Potential Vanishing at Infinity
Fabio Punzo, Marcello Svagna
We investigate the uniqueness, in suitable weighted spaces, of solutions to the Schrödinger equation with a potential, posed on infinite graphs. The potential can tend to…
Blow-up and global existence for semilinear parabolic equations on infinite graphs
Gabriele Grillo, Giulia Meglioli, Fabio Punzo
We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function …
Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators
Stefano Biagi, Fabio Punzo, Eugenio Vecchi
We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator , with a power-like source term.…
Phragmèn-Lindelöf type theorems for elliptic equations on infinite graphs
Stefano Biagi, Fabio Punzo
We investigate the validity of the Phragmèn-Lindelöf principle for a class of elliptic equations with a potential, posed on infinite graphs. Consequently, we get uniqueness, in the…
Nonexistence results for semilinear elliptic equations on weighted graphs
Dario Daniele Monticelli, Fabio Punzo, Jacopo Somaglia
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…
A Liouville theorem for elliptic equations with a potential on infinite graphs
Stefano Biagi, Giulia Meglioli, Fabio Punzo
We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on t…