Rynne, Bryan2021-04-122021-04-122004-03-03Rynne, B. P. (2004). Solution curves of 2m-th order boundary-value problems. <i>Electronic Journal of Differential Equations, 2004</i>(32), pp. 1-16.1072-6691https://hdl.handle.net/10877/13360We consider a boundary-value problem of the form Lu = (λƒ (u), where L is a 2m-th order disconjugate ordinary differential operator (m ≥ 2 is an integer), λ ∈ [0, ∞), and the function ƒ : ℝ → ℝ is C2 and satisfies ƒ(ξ) > 0, ξ ∈ ℝ. Under various convexity or concavity type assumptions on ƒ we show that this problem has a smooth curve, S0, of solutions (λ, u), emanating from (λ, 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.Text16 pages1 file (.pdf)enAttribution 4.0 InternationalOrdinary differential equationsNonlinear boundary value problemsArticle