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Journal of Lie Theory 25 (2015), No. 1, 125--146
Copyright Heldermann Verlag 2015

Side Conditions for Ordinary Differential Equations

Giampaolo Cicogna
Dipartimento di Fisica, UniversitÓ di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy

Giuseppe Gaeta
Dipartimento di Matematica, UniversitÓ degli Studi di Milano, via Saldini 50, 20133 Milano, Italy

Sebastian Walcher
Lehrstuhl A fŘr Mathematik, RWTH Aachen, 52056 Aachen, Germany

We specialize Olver's and Rosenau's side condition heuristics for the determination of particular invariant sets of ordinary differential equations. It turns out that side conditions of so-called LaSalle type are of special interest. Moreover we put side condition properties of symmetric and partially symmetric equations in a wider context. In the final section we present an application to parameter-dependent systems, in particular to quasi-steady state for chemical reactions.

Keywords: Invariant set, Lie series, infinitesimal symmetry, quasi-steady state, QSS.

MSC: 34A05, 34C14, 34C45, 92C45

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