Bryan P. Rynne
We consider a boundary-value problem of the form , where is a -th order disconjugate ordinary differential operator ( is an integer), , and the function is and satisfies , . Under various convexity or concavity type assumptions on we show that this problem has a smooth curve, , of solutions , emanating from , and we describe the shape and asymptotes of . All the solutions on are positive and all solutions for which is stable lie on .
Submitted December 15, 2003. Published March 3, 2004.
Math Subject Classifications: 34B15.
Key Words: Ordinary differential equations, nonlinear boundary value problems.
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| Bryan P. Rynne |
Edinburgh EH14 4AS, Scotland
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