Kamke's Uniqueness Theorem
نویسنده
چکیده
A generalization of Kamke's uniqueness theorem in ordinary differential equations is obtained for the limit Cauchy problem, viz x'{t) = f(t, x(t)), x{t) -> x0 as 1J10, where / and x take values in an arbitrary normed linear space X and the initial point {t0, x0) is permitted to be on the boundary of the domain of/. Kamke's hypothesis that \\f(t,x)-f{t,y)\\ < <(>(\t-to\, ||x-,y||) is replaced by a weaker dissipative-type hypothesis formulated in terms of the duality map of X and a semi-inner product derived from it. Even in the scalar case in which X = U, the generalization obtained is still an extension of Kamke's theorem and some of its later analogues.
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