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Elementary proofs of Peano's existence theorem

Published online by Cambridge University Press:  09 April 2009

M. A. Dow  and
R. Výborný
M. A. Dow
Affiliation:
Department of Mathematics University of Queensland, Australia.
R. Výborný
Affiliation:
Department of Mathematics University of Queensland, Australia.
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An “elementary” proof of Peano's existence theorem is given that, in addition to avoiding the Ascoli lemma, relies neither on Dini's theorem, nor on uniform continuity of the right hand side of φ' = f(t,φ). It is based on superfunctions. Also, another standard proof of that theorem, based on approximation of the right hand side, is made elementary.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 3 , May 1973 , pp. 366 - 372
Copyright
Copyright © Australian Mathematical Society 1973

References

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