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On the Cauchy problem for the differential equation f(t, x, x′, …, x(k)) = 0
Published online by Cambridge University Press: 18 May 2009
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In the sequel, given k, n ∈ ℕ, p ∈ [1, ∞] and a compact real interval I, we denote by Wk, p(I, ℝn) (simply by Wk,p(I if n = 1) the space of all functions u ∈ Ck−1(I, ℝn) such that uk−1 is absolutely continuous in I and u(k) ∈ Lp (I, ℝn).
Very recently, in [11], J. R. L. Webb and S. C. Welsh obtained the following existence result.
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- Copyright © Glasgow Mathematical Journal Trust 1991
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