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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalElectronic Journal of Differential Equations
Volume2004
Publication statusPublished - 3 Mar 2004

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Asymptote
Concavity
Convexity
Differential operator
Boundary Value Problem
Curve
Integer
Form

Keywords

  • Nonlinear boundary value problems
  • Ordinary differential equations

Cite this

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Solution curves of 2m-th order boundary-value problems. / Rynne, Bryan P.

In: Electronic Journal of Differential Equations, Vol. 2004, 03.03.2004, p. 1-16.

Research output: Contribution to journalArticle

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T1 - Solution curves of 2m-th order boundary-value problems

AU - Rynne, Bryan P.

PY - 2004/3/3

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N2 - 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.

AB - 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.

KW - Nonlinear boundary value problems

KW - Ordinary differential equations

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JF - Electronic Journal of Differential Equations

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