About sign-constancy of Green's functions for impulsive second order delay equations

Alexander Domoshnitsky, Guy Landsman, Shlomo Yanetz

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider the following second order differential equation with delay (Equation) In this paper we find necessary and sufficient conditions of positivity of Green's functions for this impulsive equation coupled with one or two-point boundary conditions in the form of theorems about differential inequalities. By choosing the test function in these theorems, we obtain simple sufficient conditions. For example, the inequality (Equation) is a basic one, implying negativity of Green's function of two-point problem for this impulsive equation in the case 0<γi≤1,0<δi≤1 for i = 1,..., p.

Original languageEnglish
Pages (from-to)339-362
Number of pages24
JournalOpuscula Mathematica
Volume34
Issue number2
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes

Keywords

  • Boundary value problem
  • Green's functions
  • Impulsive equations
  • Positivity/negativity of green's functions
  • Second order

ASJC Scopus subject areas

  • Mathematics (all)

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