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Zbl 0552.34023
Holmes, Philip; Spence, David
On a Painlevé-type boundary-value problem. (English)
[J] Q. J. Mech. Appl. Math. 37, 525-538 (1984). ISSN 0033-5614; ISSN 1464-3855/e

We study the existence and uniqueness of solutions to the two-point boundary value problem $y''=y\sp 2$-x with $y(0)=0$ and $y(x)\sim +\sqrt{x}$ as $x\to \infty$. 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.

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
34B10 Multipoint boundary value problems

Keywords: two-point boundary value problem; monotonically increasing solution

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