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Index Zero and Index One
Book chapter

Index Zero and Index One

David E Stewart
Dynamics with Inequalities, pp.147-205
Other Titles in Applied Mathematics, Society for Industrial and Applied Mathematics
01/01/2011
DOI: 10.1137/1.9781611970715.ch5

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Abstract

In this chapter we will consider index-zero and index-one DVIs and various special cases and generalizations. Index-zero inequalities are the easiest kind of DVI to solve since the “algebraic” part of the solution (the part where derivatives do not appear) can be found in terms of the “differential” part of the solution. Substituting this into the differential equation gives an ordinary differential equation without an unknown “algebraic” variable. Thus we can reduce these problems to the study of ordinary differential equations. Index-zero problems can typically be reduced to Lipschitz differential equations. Index-one DVIs, on the other hand, are considerably more interesting. However, index-zero problems can be used as a starting point for many different approximations and analyses of index-one and other problems.
Dynamics

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