Ah. Zemanian, THE VALIDITY OF KIRCHHOFFS LAWS FOR A CLASS OF NONLINEAR TRANSFINITE NETWORKS, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 40(7), 1993, pp. 477-482
Kirchhoff's laws hold only sometimes in transfinite networks. For nonl
inear networks, there are presently just a few preliminary results reg
arding when they do hold. This work establishes more explicit and broa
der conditions for their validity in nonlinear transfinite networks. I
t also presents a fundamental theorem for the existence and uniqueness
of the voltage-current regime in such a network. This theorem is dual
to the one currently extant.