For a scalar delay differential equation ẋ(t) + ∑k=1∞ak(t)x(hk(t)) = 0 (hk(t) ≤ t) 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.
|Number of pages||14|
|Journal||Zeitschrift fur Analysis und ihre Anwendung|
|State||Published - 1 Jan 2002|
- Delay differential equations
- Infinite number of delays
ASJC Scopus subject areas
- Applied Mathematics