Mathematics (Oct 2022)

Negativity of Green’s Functions to Focal and Two-Point Boundary Value Problems for Equations of Second Order with Delay and Impulses in Their Derivatives

  • Alexander Domoshnitsky,
  • Sergey Malev,
  • Vladimir Raichik

DOI
https://doi.org/10.3390/math10193683
Journal volume & issue
Vol. 10, no. 19
p. 3683

Abstract

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We consider the second-order impulsive differential equation with impulses in derivative and without the damping term. Sufficient conditions that a nontrivial solution of the homogeneous equation having a zero of its derivative does not have a zero itself are obtained. On the basis of the obtained results on differential inequalities, which can be considered as analogues of the Vallee–Poussin theorems, new sufficient conditions on the negativity of Green’s functions are obtained.

Keywords