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 Painlevé equations (Sect. 1.3).
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© 2016 Springer International Publishing Switzerland
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Delabaere, E. (2016). Some Elements about Ordinary Differential Equations. In: Divergent Series, Summability and Resurgence III. Lecture Notes in Mathematics, vol 2155. Springer, Cham. https://doi.org/10.1007/978-3-319-29000-3_1
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DOI: https://doi.org/10.1007/978-3-319-29000-3_1
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28999-1
Online ISBN: 978-3-319-29000-3
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