Solution curves of 2m-th order boundary-value problems

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

Rights Holder

Rights License