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On the existence of a saturated solution of the differential equation x′ = f (t, x)

Published online by Cambridge University Press:  14 February 2012

Johann Walter
Johann Walter
Affiliation:
Institut für Mathematik, der R.W.T.H. Aachen
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Synopsis

Let (1) x′ = f(t, x) be any differential equation and S0 the set of solutions of (1) with open domain. It is known that for every g ∊ S0 a non-continuable (= saturated) ∊ S0 exists which is an extension of g. Usually is represented in the form is a sequence in S0 defined by some sort of a variant of what is called ‘recursive definition’ in set theory. It will be shown that a function

exists (P(S0) is the power set of S0) such that the above-mentioned variant can be given the form: There exists a sequence in S0 such that

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 1-2 , 1977 , pp. 97 - 99
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

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