Solution curves of 2m-th order boundary-value problems
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Date
2004-03-03
Authors
Rynne, Bryan
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Ordinary differential equations, Nonlinear boundary value problems
Citation
Rynne, B. P. (2004). Solution curves of 2m-th order boundary-value problems. <i>Electronic Journal of Differential Equations, 2004</i>(32), pp. 1-16.
Rights
Attribution 4.0 International