For a scalar delay differential equation
a connection between the following four properties is established:
- non-oscillation of this equation
- non-oscillation of the corresponding differential inequality
- positiveness of the fundamental function - existence of a non-negative solution for a certain explicitly constructed nonlinear integral inequality.
Explicit non-oscillation and oscillation conditions, comparison theorems and a criterion of the existence of a positive solution are presented for this equation.
Cite this article
Leonid Berezansky, Elena Braverman, On Oscillation of a Differential Equation with Infinite Number of Delays. Z. Anal. Anwend. 21 (2002), no. 3, pp. 803–816DOI 10.4171/ZAA/1109