März, Roswitha
Criteria for the trivial solution of differential algebraic equations with small nonlinearities to be asymptotically stable
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

34A09 Implicit equations

34D20 Lyapunov stability

34A34 Nonlinear equations and systems, general

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 except for the expensive proofs.
Keywords: differential algebraic equations, initial value problems, asymptotical stability, implicit differential equations