The validity of Kirchhoff's laws for a class of nonlinear transfinite networks

摘要

Kirchhoff's laws hold only sometimes in transfinite networks. For nonlinear networks, there are presently just a few preliminary results regarding when they do hold. This work establishes more explicit and broader conditions for their validity in nonlinear transfinite networks. It 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.