A Thomson's Principle for Infinite, Nonlinear Resistive Networks

Suppose Γ is an infinite resistive electrical network with resistors of the form (2). We prove an existence and uniqueness theorem for the current generated by external current sources by establishing the analogue of Thomson's principle in suitable modular sequence spaces.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1990, Vol.109 (2), p.461-468
Main Authors: De Michele, L., Soardi, P. M.
Format: Article
Language:English
Subjects:
Banach space
Electric current
Electric potential
Electrical networks
Exact sciences and technology
Functional analysis
Hilbert spaces
Kirchhoff circuit laws
Mathematical analysis
Mathematical functions
Mathematical sequences
Mathematics
Sciences and techniques of general use
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Description
Summary:Suppose Γ is an infinite resistive electrical network with resistors of the form (2). We prove an existence and uniqueness theorem for the current generated by external current sources by establishing the analogue of Thomson's principle in suitable modular sequence spaces.
ISSN:0002-9939
1088-6826
DOI:10.1090/s0002-9939-1990-1014643-1