On the existence of a saturated solution of the differential equation x′ = f (t, x)
1977 ◽
Vol 78
(1-2)
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pp. 97-99
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SynopsisLet (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 functionexists (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
2003 ◽
Vol 9
(3)
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pp. 273-298
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1968 ◽
Vol 64
(2)
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pp. 439-446
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1986 ◽
Vol 102
(3-4)
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pp. 253-257
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1964 ◽
Vol 4
(2)
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pp. 179-194
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1995 ◽
Vol 36
(4)
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pp. 438-459
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1963 ◽
Vol 3
(2)
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pp. 202-206
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