Nonlinear, resistive, countably infinite electrical networks

∗This work was supported by NSF Grant MCS 75-05268.

†

†Dedicated to Professor A. Erdélyi on the occasion of his seventieth birthday.

Abstract

Nonlinear infinite electrical networks can be analysed by using Hilbert-space techniques when the total power in the network is finite. This work attacks the case where the total power is not finite. Graph-theoretic methods are used to show that a unique current flow occurs in a countably infinite, nonlinear, resistive network after the voltage-current pairs in certain specified branches are arbitrarily assigned. The currents and voltages throughout the entire network can be determined by computing them recursively in a sequence of finite subnetworks that partition the network. The main theorem requires that the resistances and conductances in the network satisfy sufficiently strong Lipschitz conditions.

∗This work was supported by NSF Grant MCS 75-05268.

†Dedicated to Professor A. Erdélyi on the occasion of his seventieth birthday.

∗This work was supported by NSF Grant MCS 75-05268.

†Dedicated to Professor A. Erdélyi on the occasion of his seventieth birthday.

Notes

∗This work was supported by NSF Grant MCS 75-05268.

†Dedicated to Professor A. Erdélyi on the occasion of his seventieth birthday.

Additional information

Notes on contributors

A. H. Zemanian