A Non-Local Quasi-Linear Ground State Representation and Criticality Theory

2022/04/11 by Florian Fischer, Fischer, Florian · 1 citation
Mathematics · #31C45 #35R02 (Secondary) #39A12 (Primary) 31C20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2204.05391

openalex publication_date 2022/04/11 · openalex created_date 2022/04/15 · openalex updated_date 2026/07/28

Abstract

We study energy functionals associated with non-local quasi-linear Schrödinger operators, and develop a ground state representation. Our main focus is on infinite graphs but we also consider non-local quasi-linear Schrödinger operators in the Euclidean space. Using the representation, we develop a criticality theory for quasi-linear Schrödinger operators on general weighted graphs, and show characterisations for a Hardy inequality to hold true. As an application, we show a Liouville comparison principle on graphs.

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