On the existence of nonoscillatory solutions of three-dimensional time scale systems

Öztürk, Özkan

doi:10.1007/s11784-017-0454-9

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…In addition to that, we obtain the existence of nonoscillatory solutions of system (1.1) which is not studied in [3]. Some other versions of two and three dimensional time scale systems and delay time-scale systems are considered in [1,[11][12][13], respectively. We also suggest [4] for the continuous case, [7,8,10,14] for the discrete case and the books [5,6] by Bohner and Peterson about the theory of time scales.…”

Section: ∆T T ∈ Tmentioning

confidence: 92%

On nonoscillatory solutions of three dimensional time-scale systems

Akin¹,

Hassan²,

Öztürk³

et al. 2019

Turk J Math

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Section: ∆T T ∈ Tmentioning

confidence: 92%

On nonoscillatory solutions of three dimensional time-scale systems

Akin¹,

Hassan²,

Öztürk³

et al. 2019

Turk J Math

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“…ÀÁ is a solution of (16) in N c such that xt ðÞ!∞, yt ðÞ!3 and zt ðÞ!0ast ! ∞, i.e., N c ∞,B,0 6 ¼ ∅ by Theorem 3.8 (i).…”

Section: Existence In N Bmentioning

confidence: 99%

Existence and Asymptotic Behaviors of Nonoscillatory Solutions of Third Order Time Scale Systems

Öztürk¹

2021

Recent Developments in the Solution of Nonlinear Differential Equations

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Nonoscillation theory with asymptotic behaviors takes a significant role for the theory of three-dimensional (3D) systems dynamic equations on time scales in order to have information about the asymptotic properties of such solutions. Some applications of such systems in discrete and continuous cases arise in control theory, optimization theory, and robotics. We consider a third order dynamical systems on time scales and investigate the existence of nonoscillatory solutions and asymptotic behaviors of such solutions. Our main method is to use some well-known fixed point theorems and double/triple improper integrals by using the sign of solutions. We also provide examples on time scales to validate our theoretical claims.

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“…One of the reasons for this is a necessity for some techniques which can be used in investigating equations arising in mathematical models that describe real life situations in population biology, economics, probability theory, genetics, psychology, and so forth, see [3,5,8,9]. Also, similar works in two and three dimensions (limit behaviors) for more general cases, i.e., continuous and discrete cases, have been done by some authors, see [1,[11][12][13]16]. There are many papers in which systems of difference equations have been studied, as in the examples given below.…”

Section: Introductionmentioning

confidence: 99%