Abstract
This paper summarizes so far obtained results on the number of solutions of a class of nonlinear equations related to nonlinear circuits. One of the most well-known results on this problem is the Sandberg-Willson theorem, where the nonlinear functions are assumed to be monotone. In this report we discuss the same problem under more practical conditions and show more general results obtained by a series of papers by the author. The results can be described by use of a new notion, "Ω-matrix", which is introduced in Section 2. In the third section we rst describe the Sandberg-Willson theorem and then we discuss our nonlinear equation problem and especially about a "solution curve" corresponding to the equation and describe how the problem on the number of solutions closely relates to the Ω-matrix.
