Small solutions of nonlinear differential equations near branching points (Q647875)
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scientific article; zbMATH DE number 5975542
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Small solutions of nonlinear differential equations near branching points |
scientific article; zbMATH DE number 5975542 |
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Small solutions of nonlinear differential equations near branching points (English)
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21 November 2011
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The authors consider scalar implicit ordinary differential equations of arbitrary order in the neighbourhood of a branching point and construct parametric families of small solutions. They first analyse the Newton diagrams of homogeneous components of the equation and then use the results for a reduction to a first-order system of equations with a regular singularity. In addition, they describe a technique for determining the asymptotic behaviour of their solution family.
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implicit ordinary differential equation
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branching point
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Newton diagram
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regular singularity
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asymptotics
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0.91691834
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0.89400953
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0.8938698
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0.8845006
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