Abstract
AbstractWe study energy functionals associated with quasi-linear Schrödinger operators on infinite weighted graphs, and develop a ground state representation. Using the representation, we develop a criticality theory, and show characterisations for a Hardy inequality to hold true. As an application, we show a Liouville comparison principle.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference62 articles.
1. Abdellaoui, B., Mahmoudi, F.: An improved Hardy inequality for a nonlocal operator. Discrete Contin. Dyn. Syst 36(3), 1143–1157 (2016)
2. Alexander, A., Balinsky, W., Desmond, Evans., and Lewis, Roger T.: The analysis and geometry of Hardy’s inequality, pp. xv+263. Universitext. Springer, Cham (2015)
3. Allegretto, W.: On the equivalence of two types of oscillation for elliptic operators. Pacific J. Math. 55, 319–328 (1974)
4. Allegretto, W., Xi, H.Y.: A Picone’s identity for the p-Laplacian and applications. Nonlinear Anal. 32(7), 819–830 (1998)
5. Amghibech, S.: On the discrete version of Picone’s identity. Discrete Appl. Math. 156(1), 1–10 (2008)
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