×

Hardy fields. (English) Zbl 0518.12014


MSC:

12H20 Abstract differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
32B10 Germs of analytic sets, local parametrization
14Pxx Real algebraic and real-analytic geometry
Full Text: DOI

References:

[1] Bellman, R., Stability Theory of Differential Equations (1953), McGraw-Hill: McGraw-Hill New York · Zbl 0052.31505
[2] Bourbaki, N., Fonctions d’une Variable Réele, (Étude Locale des Fonctions (1961), Hermann: Hermann Paris), Chapter V · Zbl 0346.26003
[3] du Bois-Reymond, P., Ueber asymptotische Werthe, infinitäre Approximationen und infinitäre Auflösung von Gleichungen, Math. Ann., 8, 362-414 (1875) · JFM 07.0249.01
[4] Hardy, G., Some results concerning the behaviour at infinity of a real and continuous solution of an algebraic differential equation of the first order, (Proc. London Math. Soc. Ser. 2, 10 (1912)), 451-468 · JFM 43.0390.02
[5] Hardy, G., Orders of Infinity (1924), Cambridge Univ. Press: Cambridge Univ. Press London/New York · JFM 50.0153.04
[6] Lightstone, A.; Robinson, A., Nonarchimedian Fields and Asymptotic Expansions (1975), North-Holland: North-Holland Amsterdam, and Amer. Elsevier, New York · Zbl 0303.26013
[7] Marić, V., Asymptotic behavior of solutions of a nonlinear differential equation of the first order, J. Math. Anal. Appl., 38, 187-192 (1972) · Zbl 0233.34066
[8] Olver, F., Asymptotics and Special Functions (1974), Academic Press: Academic Press New York · Zbl 0303.41035
[9] Robinson, A., On the real closure of a Hardy field, (Asser, G.; etal., Theory of Sets and Topology (1972), Deut. Verlag Wissenschaften: Deut. Verlag Wissenschaften Berlin) · Zbl 0298.02061
[10] Singer, M., Asymptotic Behavior of Solutions of Differential Equations and Hardy Fields, (Preliminary report (1976), SUNY: SUNY Stone Brook), unpublished
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.