Differential equations with bounded positive Green's functions and generalized Aizerman's hypothesis

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4 Scopus citations

Abstract

We derive conditions for the positivity and boundedness of the Green functions of the higher order linear nonautonomous ODE. By virtue of these conditions, the existence of positive solutions for a class of non-linear equations is proved. In addition, upper and lower estimates for the Green functions are established. Moreover, it is shown that nonlinear equations, having separated nonautonomous linear parts, satisfy the generalized Aizerman hypothesis on absolute stability, if they have the positive Green functions.

Original languageEnglish
Pages (from-to)137-150
Number of pages14
JournalNonlinear Differential Equations and Applications
Volume11
Issue number2
DOIs
StatePublished - 1 Jan 2004

Keywords

  • Green's function
  • Linear and nonlinear ordinary differential equations
  • Positivity
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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