Book Chapter10.1007/978-3-319-29000-3_1
Some Elements about Ordinary Differential Equations
Eric Delabaere
- 01 Jan 2016
- pp 1-14
TL;DR: The main differences between solutions of linear versus nonlinear ODEs, when the question of their analytic continuation is considered, are discussed in this paper, and the fundamental existence theorem for Cauchy problems is given.
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Abstract: This chapter is merely devoted to recalling usual notation and elementary results on ordinary differential equations in the complex domain. We give the fundamental existence theorem for Cauchy problems (Sect. 1.1). We detail the main differences between solutions of linear versus nonlinear ODEs, when the question of their analytic continuation is considered (Sect. 1.2). Finally we provide a short introduction to Painleve equations (Sect. 1.3).
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Ordinary differential equations
Philip Hartman
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Peter D. Lax
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TL;DR: In this article, a general principle for associating nonlinear equations evolutions with linear operators so that the eigenvalues of the linear operator integrals of the nonlinear equation can be found is presented, where the main tool used is the first remarkable series of integrals discovered by Kruskal and Zabusky.
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