Criteria for the trivial solution of differential algebraic equations with small nonlinearities to be asymptotically stable

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. (C) 1998 Academic Press.