Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales

Zhu, Shuqian; Sheng, Chunyun

doi:10.1155/2012/137471

Cited by 5 publications

(3 citation statements)

References 22 publications

(2 reference statements)

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“…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

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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.

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“…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

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

Section: Introductionmentioning

confidence: 99%

Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

Öztürk

Akın

2016

Nonautonomous Dynamical Systems

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“…In fact, there are numerous theories used for solving various nonlinear vibration problems (e.g., [25][26][27][28][29][30][31][32][33][34][35]). In some approaches for solving the problems of large amplitude structure or nonlinear oscillation (e.g., [36][37][38][39]), they require a significant effort in the tedious eigenvalue solution steps. The present study uses the proposed elliptical integral method to develop a concise elliptical integral solution for the large amplitude free vibration analysis.…”

Section: Introductionmentioning

confidence: 99%

Natural Frequency Analysis of Two Nonlinear Panels Coupled with a Cavity Using the Approximate Elliptic Integral Solution and the Method of Harmonic Residual Minimization

Lee

2015

Discrete Dynamics in Nature and Society

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The nonlinear structural acoustic problem considered in this study is the nonlinear natural frequency analysis of flexible double panels using the elliptic integral solution method. There are very limited studies for this nonlinear structural-acoustic problem, although many nonlinear plate or linear double panel problems have been tackled and solved. A multistructural/acoustic modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibrations of the flexible panels and acoustic pressure induced within the air gap. One is the von Karman’s plate equation and the other is the homogeneous wave equation. The results obtained from the proposed method approach are verified with those from a numerical method. The effects of vibration amplitude, gap width, aspect ratio, the numbers of acoustic modes and harmonic terms, and so forth on the resonant frequencies of the in-phase and out of phase modes are examined.

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Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales

Cited by 5 publications

References 22 publications

On Nonoscillatory Solutions of Two-Dimensional Nonlinear Dynamical Systems

On Nonoscillatory Solutions of Two-Dimensional Nonlinear Dynamical Systems

Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

Natural Frequency Analysis of Two Nonlinear Panels Coupled with a Cavity Using the Approximate Elliptic Integral Solution and the Method of Harmonic Residual Minimization

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