The existence and uniqueness of node voltages in a non-linear resistive transfinite electrical network

Transfinite resistive electrical networks have unique voltage-current regimes under very broad conditions on their resistances and source values; this has been established previously. However, as is shown by example in this paper, such networks need not have unique node voltages with respect to a chosen ground node either because the voltages along every path from ground to another chosen node may not be summable or because the voltages along two such paths to the same node may be summable but with different sums. A second result of this work is the establishment of a sufficient set of conditions for the existence and uniqueness of node voltages in a non-linear transfinite network. The theory of modular sequence spaces is used for this purpose.