Oscillation criteria for two-dimensional systems of first-order linear dynamic equations on time scales

Anderson, Douglas R.; Hall, William R.

doi:10.2140/involve.2009.2.1

Cited by 9 publications

(14 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the following lemma was proved by Anderson [1] for the component functions x and y in the case c(t) ≡ 0 , we skip the proof because they are very similar. …”

Section: Proposition 4 (Integration By Parts) [3 Theorem 177 Vi] Ifmentioning

confidence: 99%

On Oscillation of Two-Dimensional Time-Scale Systems with a Forcing Term

Öztürk¹

2018

Turk J Math

View full text Add to dashboard Cite

show abstract

“…Since the following lemma was proved by Anderson [1] for the component functions x and y in the case c(t) ≡ 0 , we skip the proof because they are very similar. …”

Section: Proposition 4 (Integration By Parts) [3 Theorem 177 Vi] Ifmentioning

confidence: 99%

On Oscillation of Two-Dimensional Time-Scale Systems with a Forcing Term

Öztürk¹

2018

Turk J Math

View full text Add to dashboard Cite

show abstract

“…Recent advances in oscillation and nonoscillation criteria for two-dimensional time scale systems have been studied in Refs. [29][30][31].…”

Section: Dynamical Systems On Time Scalesmentioning

confidence: 99%

On Nonoscillatory Solutions of Two-Dimensional Nonlinear Dynamical Systems

Akın¹,

Öztürk²

2017

Dynamical Systems - Analytical and Computational Techniques

View full text Add to dashboard Cite

During the past years, there has been an increasing interest in studying oscillation and nonoscillation criteria for dynamical systems on time scales that harmonize the oscillation and nonoscillation theory for the continuous and discrete cases in order to combine them in one comprehensive theory and eliminate obscurity from both. We not only classify nonoscillatory solutions of two-dimensional systems of first-order dynamic equations on time scales but also guarantee the existence of such solutions using the Knaster, Schauder-Tychonoff and Schauder's fixed point theorems. The approach is based on the sign of components of nonoscillatory solutions. A short introduction to the time scale calculus is given as well. Examples are significant in order to see if nonoscillatory solutions exist or not. Therefore, we give several examples in order to highlight our main results for the set of real numbers R, the set of integers Z and q N 0 = {1, q, q 2 , q 3 , …}, q >1, which are the most well-known time scales.

show abstract

“…Oscillation and nonoscillation criteria for two-dimensional time scale systems have been studied by [1], [5], [8], [11,12].…”

Section: Introductionmentioning

confidence: 99%