Kamke's Uniqueness Theorem

@article{Ramankutty1980KamkesUT,
  title={Kamke's Uniqueness Theorem},
  author={Padmaja Ramankutty},
  journal={Journal of The London Mathematical Society-second Series},
  year={1980},
  pages={110-116}
}
  • Padmaja Ramankutty
  • Published 1980
  • Mathematics
  • Journal of The London Mathematical Society-second Series
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… Expand
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