First order differential closures of certain partially ordered fields
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- by Joseph E. Turcheck PDF
- Trans. Amer. Math. Soc. 195 (1974), 97-114 Request permission
Abstract:
First order algebraic differential equations (a.d.e.’s) are considered in the setting of an abstract differential field with an abstract order relation, whose properties mirror those of the usual asymptotic dominance relations of analysis. An abstract existence theorem, for such equations, is proved by constructing an extension of both the differential field and the abstract order relation. As a consequence, a first order differential closure theorem, for those differential fields with order relations which we consider, is obtained. The closure theorem has corollaries which are important to the asymptotic theory of a.d.e.’s and have application to a.d.e.’s with coefficients meromorphic in a sector of the complex plane.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 195 (1974), 97-114
- MSC: Primary 12H05; Secondary 02H15
- DOI: https://doi.org/10.1090/S0002-9947-1974-0340229-3
- MathSciNet review: 0340229