Displaying similar documents to “Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations”

Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations

John Shackell (1995)

Annales de l'institut Fourier

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We consider the asymptotic growth of Hardy-field solutions of algebraic differential equations, e.g. solutions with no oscillatory component, and prove that no ‘sub-term’ occurring in a nested expansion of such can tend to zero more rapidly than a fixed rate depending on the order of the differential equation. We also consider series expansions. An example of the results obtained may be stated as follows. Let g be an element of a Hardy field which has an asymptotic series...