Existence, Uniqueness and Determination of Solution of Certain Piecewise Linear Resistive Networks

For an equation o-f the -form £<&.>••¥., it is shown that there is at least one solution •for every y_ if F_ is eventually PB passive or the e-f-fective Jacobian matrix in all the unbounded regions is a P matrix. In addition to this, i-f the Jacobian determinant has the same sign in all the regions, then F is a homeomorphism. For equations o-f the form E is onto if H is Po anci F_"A Q.. It is also shown that, roughly under these conditions, the generalised Katzenelson's method converges to a solution. Homeomorphism of these two forms is guaranteed if the Jacobian determinant has the same sign in all the regions in addition to the above conditions.