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 |