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

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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

Keywords

  • Nonlinear boundary value problems
  • Ordinary differential equations

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