Third Order Differential Equations with Fixed Critical Points

Abstract

where ai (i = 0, 1, . . . , 8) are analytic functions of the complex variable x. The object of this article is to find necessary and sufficient conditions about the coefficients ai (i = 0, 1, . . . , 8) in order that the only movable singularities of solutions of (1.1) may be poles. Definition 1. We say that a differential equation belong to the class M if and only if the only movable singularities of her solutions are poles. Notation. We will denote by T (λ, μ, φ) a transformation defined by: { v(x) = λ(x)u(t) + μ(x) t = φ(x) (1.2)

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Cite this paper

@inproceedings{ATMOKHTAR2007ThirdOD, title={Third Order Differential Equations with Fixed Critical Points}, author={SADJIA A{\"{I}T-MOKHTAR and Michel Cr{\'e}peau}, year={2007} }