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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The failure in computable analysis of a classical existence theorem for differential equations


Author: Oliver Aberth
Journal: Proc. Amer. Math. Soc. 30 (1971), 151-156
MSC: Primary 34A10; Secondary 02E15
MathSciNet review: 0302982
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Abstract: An example is given of a uniformly continuous constructive function $ f(x,y)$ with $ f(0,0) = 0$, such that the differential equation $ y' = f(x,y)$ with the initial condition $ y(0) = 0$ has no constructive solution.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0302982-7
PII: S 0002-9939(1971)0302982-7
Keywords: Computable analysis, constructive function, computable number, program, Peano's Theorem, derivative, Lipschitz condition
Article copyright: © Copyright 1971 American Mathematical Society