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Seminar on analytic theory of differential equations
February 1, 2017 14:30, Moscow, Steklov Mathematical Institute, Room 440 (8 Gubkina)
 


On the divergence of an asymptotic expansion of a solution to the third Painlevé equation

A. V. Vasilyev
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A. V. Vasilyev


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Abstract: We find formal asymptotics for solutions of the third Painlevé equation near infinity, in particular, a formal Puiseux series expansion. This series is an asymptotic expansion of a genuine solution and belongs to the Gevrey class of order 1 (after reducing it to a power series). We obtain a family of the equation parameters such that estimates for the coefficients of the Gevrey series under consideration are exact, hence the series diverges.

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