Abstract
We consider nonlinear resistive networks. The equivalence of the Liouville property, the Khas'minskii condition and the weak maximum principle for operators of Laplacian with potential is proved, and a number of criteria for these properties are given. The parabolicity of networks is also discussed.
Funding Statement
The second author is partially supported by the Grant-In-Aid for Scientific Research (C) 16K05124 and Scientific Research (A) 17H01092 of the Japan Society for the Promotion of Science.
Acknowledgment
We would like to thank the referee for careful readings of the manuscript and valuable comments that improved the exposition.
Citation
Tae HATTORI. Atsushi KASUE. Motoki OHKUBO. "Some function theoretic properties of nonlinear resistive networks." Hokkaido Math. J. 50 (3) 409 - 454, October 2021. https://doi.org/10.14492/hokmj/2019-196
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