Abstract
The existence question for a nonlinear, two point boundary value problem (continuous and Lipschitzian) can be reduced to that of the corresponding unforced problem with one zero boundary condition. For fixed left-hand end point, the set of right-hand end points for which existence fails consists of isolated points and isolated intervals.Certain bounding curves arise in the case of failure of existence for an interval of right-hand end points, and smoothness and dependence on initial conditions of these curves are determined in part. Also some relationships between the given problem and the problem with initial and terminal points reversed are established.
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