On \(n\)th order differential equations over Hardy fields. (English) Zbl 0822.34033

A Hardy field is a set of germs of real valued functions on positive half lines in \(\mathbb{R}\) that is closed under differentiation and forms a field with respect to the addition and multiplication. The author’s results concern \(n\)th order differential equations over Hardy fields; for example, there is given a necessary and sufficient condition for a nonhomogeneous \(n\)th order linear ordinary differential equation over a perfect Hardy field to be nonoscillatory.


34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
26A12 Rate of growth of functions, orders of infinity, slowly varying functions
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