Positive solutions of nonlinear three-point boundary-value problems

Ruyun Ma, Haiyan Wang

Research output: Contribution to journalArticle

80 Scopus citations

Abstract

Let a ∈ C[0, 1], b ∈ C([0, 1], (-∞, 0]). Let φ1 (t) be the unique solution of the linear boundary value problem u″(t) + a(t)u′(t) + b(t)u(t) = 0, t ∈ (0,1), u(0) = 0, u(1) = 1. We study the existence of positive solutions to the nonlinear boundary-value problem u″(t) + a(t)u′(t) + b(t)u(t) + h(t)f(u) = 0, t ∈ (0,1), u(0) = 0, αu(η) = u(1). where 0 < η < 1 and 0 < αφ1(η) < 1 are given, h ∈ C([0, 1], [0, ∞)) satisfying that there exists x0 ∈ [0, 1] such that h(x0) > 0, and f ∈ C([0, ∞), [0, ∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.

Original languageEnglish (US)
Pages (from-to)216-227
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume279
Issue number1
DOIs
StatePublished - May 1 2003

Keywords

  • Cone
  • Fixed point
  • Positive solution
  • Second-order multi-point BVP

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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