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The Quarterly Journal of Mechanics and Applied Mathematics 1984 37(4):525-538; doi:10.1093/qjmam/37.4.525
© 1984 by Oxford University Press
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ON A PAINLEVÉ-TYPE BOUNDARY-VALUE PROBLEM

PHILIP HOLMES and DAVID SPENCE

( Department of Theoretical and Applied Mechanics and Center for Applied Mathematics, Cornell University Ithaca, NY 14853, U.S.A.
Department of Mathematics, Imperial College of Science and Technology London SW7 2BZ )

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) {small tilde} + {surd}x as x-> {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.


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