On the solvability of DC equations and the implicit integration formula

✍ Scribed by Tamás Roska; János Klimó

• Publisher: John Wiley and Sons
• Year: 1973
• Tongue: English
• Weight: 364 KB
• Volume: 1
• Category: Article
• ISSN: 0098-9886
• DOI: 10.1002/cta.4490010307

✦ Synopsis

Abstract

The paper contains the following new results concerning the solvability of the DC equations and the implicit integration formula of a broad class of nonlinear networks.

A new method of proof is given.

Conditions are given for checking the unique solvability of the DC equation F(x)+Ax = b in case of monotone (not strictly monotone) and ‘steep’ characteristics and in the case when the characteristics have negative slope. Furthermore existence theorems are given under very weak conditions.

In the case of a broad class of nonlinear networks sufficient conditions are presented for the unique solvability of the implicit integration formula when the characteristics are monotone or have negative slope.

Some practical consequences of the theorems are also discussed.