We study the existence and uniqueness of solutions to the two-point boundary-value problem y″ = y2 – x with y(0) = 0 and y(x) ˜ + √x as x→ ∞ We establish uniqueness of a monotonically increasing solution and demonstrate the existence of at least one solution with a single minimum. We conjecture that this also is unique, and support our conjecture with partially numerical arguments.

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