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Quasi-Linear Criticality Theory and Green's Functions on Graphs by Fischer, Florian is a scholarly article available to read on EtoBox.

What is Quasi-Linear Criticality Theory and Green's Functions on Graphs about?

We study energy functionals associated with quasi-linear Schr\"odinger operators on infinite graphs, and develop characterisations of (sub-)criticality via Green's functions, harmonic functions of minimal growth and capacities. We proof a quasi-linear version of the Agmon-Allegretto-Piepenbrink theorem, which says that the energy functional is non-negative if and only if there is a positive superharmonic function. Furthermore, we show that a Green's function exists if and only if the energy functional is subcritical. Comparison principles and maximum principles are the main tools in the proofs.

Author

Fischer, Florian

Published

2022

Language

EN