Growth estimates for exp—log functions

Shackell, John

doi:10.1016/s0747-7171(08)80161-7

Cited by 28 publications

(27 citation statements)

References 13 publications

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“…This is shown by the following example, adapted from one in [17]. Consider the differential equation (12) dy -= y v /…”

Section: Smaller Comparability Classesmentioning

confidence: 98%

“…Clearly F == max{7(a*), 7(111),... ,7(nj)}, and so by the choice of J, R{g) contains an element of comparability class at least F. The proof of the lemma uses arguments similar to those in [12]. However matters are simpler here because we are dealing with elements given as nested forms.…”

Section: We Define R^ By T^j = R^-i and Ta(va) = Exp(ta_i(w^)) = Exp(h)mentioning

confidence: 99%

“…Before commencing our main section, we give the ^-function notation from [12]. Let t be an element of a Hardy field with t -> 0.…”

Section: (6^+6^/3;+•••)mentioning

confidence: 99%

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

Shackell¹

1995

Annales De L’institut Fourier

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“…This is shown by the following example, adapted from one in [17]. Consider the differential equation (12) dy -= y v /…”

Section: Smaller Comparability Classesmentioning

confidence: 98%

Section: We Define R^ By T^j = R^-i and Ta(va) = Exp(ta_i(w^)) = Exp(h)mentioning

confidence: 99%

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

Shackell¹

1995

Annales De L’institut Fourier

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“…In fact, much more is true in %?. In [10] an algorithm is given for expressing elements of ŵ hich tend to infinity in the form (3) es(lPo°---lPkk{c + e)),…”

Section: Introductionmentioning

confidence: 99%

Rosenlicht fields

Shackell¹

1993

Trans. Amer. Math. Soc.

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Abstract. Let satisfy an algebraic differential equation over R. We show that if also belongs to a Hardy field, it possesses an asymptotic form which must be one of a restricted number of types. The types depend only on the order of the differential equation. For a particular equation the types are still more restricted. In some cases one can conclude that no solution of the given equation lies in a Hardy field, and in others that a particular asymptotic form is the only possibility for such solutions. This therefore gives a new method for obtaining asymptotic solutions of nonlinear differential equations. The techniques used are in part derived from the work of Rosenlicht in Hardy fields.

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“…The rest of the paper is devoted to proving Theorem 1. In Section 2 we introduce some notation and results, mainly from [17]. The proof proper begins in Section 3.…”

Section: Introductionmentioning

confidence: 99%