Existence and Uniqueness of Solutions for the Equations of Nonlinear DC Networks

摘要: Several theorems are proved concerning the existence and uniqueness of solutions equation $AF( x ) + Bx = c$, in which A B $n \times n$ matrices real numbers, c is a n-vector, $F( \equiv [ f_1 ( x_1 ), \cdots ,f_n x_n ]^T $ “diagonal” nonlinear mapping n-dimensional Euclidean space $E^n into itself. For case functions $f_k continuous, strictly monotone increasing mappings $E^1 (but not necessarily onto$E^1 $) for large important class pairs $( A,B )$, we give necessary sufficient conditions global inverse \cdot B$. not-necessarily-monotone (tunnel-diode type functions, example) guarantee at least one solution c$ each $c \in E^n $.Several significant network-theoretic implications results discussed. example, present cond...