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- Title
Comparison theorems and necessary/sufficient conditions for the existence of nonoscillatory solutions of forced impulsive differential equations with delay.
- Authors
Huang, Shao; Cheng, Sui
- Abstract
In 1997, A. H. Nasr provided necessary and sufficient conditions for the oscillation of the equationwhere η > 0, p, and g are continuous functions on [0,∞) such that p( t) ≥ 0, g( t) ≤ t, g′( t) ≥ α > 0, and lim g( t) =∞. It is important to note that the condition g′( t) ≥ α > 0 is required. In the paper, we remove this restriction under the superlinear assumption η > 1. In fact, we can do even better by considering impulsive differential equations with delay and obtain necessary and sufficient conditions for the existence of nonoscillatory solutions and also a comparison theorem that enables us to apply known oscillation results for impulsive equations without forcing terms to get oscillation criteria for the analyzed equations.
- Subjects
IMPULSIVE differential equations; NUMERICAL solutions to differential equations; DELAY differential equations; OSCILLATION theory of differential equations; CONTINUOUS functions; REAL numbers; INTEGERS
- Publication
Ukrainian Mathematical Journal, 2013, Vol 64, Issue 9, p1403
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-013-0724-7