Secondary gravitational keyholes are searched for by importance sampling: Virtual asteroid trajectories (or rather their ‘initial’ values at the time of the first encounter) are sampled according to their likelihood given the observations of the asteroid.
More generally, the unknown function y can take values on infinite dimensional spaces, such as Banach spaces or spaces of distributions.
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Hiroshi Okamura obtained a necessary and sufficient condition for the solution of an initial value problem to be unique.
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A singular solution ys(x) of an ordinary differential equation is a solution that is singular or one for which the initial value problem (also called the Cauchy problem by some authors) fails to have a unique solution at some point on the solution.
Solutions which are singular in the sense that the initial value problem fails to have a unique solution need not be singular functions.