Criteria for the Trivial Solution of Differential Algebraic Equations with Small Nonlinearities to be Asymptotically Stable

Abstract

Differential algebraic equations consisting of a constant coefficient linear part and a small nonlinearity are considered. Conditions that enable linearizations to work well are discussed. In particular, for index-2 differential algebraic equations, there results a kind of Perron Theorem that sounds as clear as its classical model. © 1998 Academic Press.