Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem

John R. Graef, Lingju Kong, Haiyan Wang

Research output: Contribution to journalArticle

87 Scopus citations

Abstract

The authors consider the boundary value problem{(y - ρ2 y + λ g (t) f (y) = 0, 0 ≤ t ≤ 2 π,; y (0) = y (2 π), y (0) = y (2 π) .) Under different combinations of superlinearity and sublinearity of the function f, various existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of λ. The uniqueness of solutions and the dependence of solutions on the parameter λ are also studied. The results are illustrated with an example.

Original languageEnglish (US)
Pages (from-to)1185-1197
Number of pages13
JournalJournal of Differential Equations
Volume245
Issue number5
DOIs
StatePublished - Sep 1 2008

Keywords

  • Dependence on a parameter
  • Existence of positive solutions
  • Krasnosel'skii's theorem
  • Multiplicity of positive solutions
  • Periodic boundary value problem

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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