ON A PAINLEVÉ-TYPE BOUNDARY-VALUE PROBLEM

1 January 1984

journal article
Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics

Vol. 37 (4) , 525-538
https://doi.org/10.1093/qjmam/37.4.525

Abstract

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.

Keywords

BOUNDARY VALUE
VALUE PROBLEM
CONJECTURE
ESTABLISH UNIQUENESS
SINGLE MINIMUM
TWO POINT
PARTIALLY NUMERICAL
NUMERICAL ARGUMENTS
PAINLEVÉ TYPE

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