| Abstract: | The properties of the solutions of the differential equation y″ = y2 ? x2 ? c subject to the condition that y is bounded for all finite x discussed. The arguments of Holmes and Spence have been used by Ockendon, Ockendon, and Johnson to show that there are no solutions if c is large and negative. Numerically we find that solutions exist provided c is greater than a critical value c* and estimate this value to be c* = ?…. As x tends to + ∞ the solutions are asymptotic to  . The relation between A+ and ?+ are found analytically as A+ → ∞. This problem arises as a connection problem in the theory of resonant oscillations of water waves. |
