Nonoscillation interval for nth order functional differential equations

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Abstract

Nonoscillation plays an important role in the theory of ordinary differential equations, but for functional differential equations and their important class such as delay differential equations, nonoscillation is defined only as the existence of an eventually positive solution on the semiaxis and cannot be used in the analysis of boundary value problems. The use of Azbelev's definition of homogeneous equations allows us to deal with the standard notion of the nonoscillation interval and to obtain results about the existence and uniqueness of the solutions for the interpolation boundary value problems and sign behavior of their Green's functions.

Original languageEnglish
Pages (from-to)e2449-e2456
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number12
DOIs
StatePublished - 15 Dec 2009

Keywords

  • Boundary value problems
  • Delay equations
  • Functional differential equations
  • Green's function
  • Nonoscillation interval
  • Normal chain of Wronskians
  • Wronskian

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