Abstract
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.
Original language | English |
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Pages (from-to) | 803-816 |
Number of pages | 14 |
Journal | Zeitschrift für Analysis und ihre Anwendungen |
Volume | 21 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jan 2002 |
Keywords
- Delay differential equations
- Infinite number of delays
- Non-oscillation
- Oscillation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics