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The method of averaging and functional differential equations with delay. (English) Zbl 0994.34054

Summary: The author presents a natural extension of the method of averaging to fast oscillating functional-differential equations with delay. Unlike the usual approach, where the analysis is kept in an infinite-dimensional Banach space, this analysis is achieved in \(\mathbb{R}^n\). The results are formulated in classical mathematics. They are proved within interval set theory which is an axiomatic description of nonstandard analysis.

MSC:

34K11 Oscillation theory of functional-differential equations
34E18 Methods of nonstandard analysis for ordinary differential equations
34C29 Averaging method for ordinary differential equations
34K25 Asymptotic theory of functional-differential equations
34K20 Stability theory of functional-differential equations
03H05 Nonstandard models in mathematics