We consider a boundary-value problem of the form Lu = ?f(u), where L is a 2m-th order disconjugate ordinary differential operator (m = 2 is an integer), ? ? [0, 8), and the function f : R ? R is C2 and satisfies f(?) > 0, ? ? R. Under various convexity or concavity type assumptions on f we show that this problem has a smooth curve, S0, of solutions (?,u), emanating from (?, u) = (0, 0), and we describe the shape and asymptotes of S0. All the solutions on S0 are positive and all solutions for which u is stable lie on S0.
|Number of pages||16|
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 3 Mar 2004|
- Nonlinear boundary value problems
- Ordinary differential equations