Abstract
Differential equations ·x( t) = f(x( t), t) are exhibited in a general infinite-dimensional Banach space, failing each of the following in turn. (i) The set S t of solution values x( t) from a given point x(0) is compact. (ii) S t is connected. (iii) Any point on the boundary ∂S t of S t can be reached by a solution x with x( s) ϵ ∂ S s , 0 ⩽ s ⩽ t.
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