On the oscillation of fourth order strongly superlinear and strongly sublinear dynamic equations

2013 ◽  
Vol 44 (1-2) ◽  
pp. 119-132 ◽  
Author(s):  
Said R. Grace ◽  
Shurong Sun ◽  
Yizhuo Wang
Keyword(s):  
Fourth Order ◽  
Dynamic Equations ◽  
Strongly Sublinear

Oscillation Theorems for Fourth-Order Half-Linear Delay Dynamic Equations with Damping

2013 ◽  
Vol 11 (2) ◽  
pp. 463-475 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Tongxing Li ◽  
Chenghui Zhang
Keyword(s):  
Fourth Order ◽  
Dynamic Equations ◽  
Linear Delay ◽  
Delay Dynamic Equations ◽  
Oscillation Theorems

Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations

2009 ◽  
Vol 14 (8) ◽  
pp. 3463-3471 ◽  
Author(s):  
Said R. Grace ◽  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Donal O’Regan
Keyword(s):  
Second Order ◽  
Dynamic Equations ◽  
Strongly Sublinear

scholarly journals Existence of nonoscillatory solutions tending to zero of fourth-order nonlinear neutral dynamic equations on time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yang-Cong Qiu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Nonoscillatory Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations

AbstractIn this paper, a class of fourth-order nonlinear neutral dynamic equations on time scales is investigated. We obtain some sufficient conditions for the existence of nonoscillatory solutions tending to zero with some characteristics of the equations by Krasnoselskii’s fixed point theorem. Finally, two interesting examples are presented to show the significance of the results.

scholarly journals Oscillation results for fourth-order nonlinear dynamic equations

2012 ◽  
Vol 25 (12) ◽  
pp. 2058-2065 ◽  
Author(s):  
Chenghui Zhang ◽  
Tongxing Li ◽  
Ravi P. Agarwal ◽  
Martin Bohner
Keyword(s):  
Fourth Order ◽  
Nonlinear Dynamic ◽  
Dynamic Equations ◽  
Nonlinear Dynamic Equations

Numerical integration of rotation with geometry propagators

2016 ◽  
Vol 07 (03) ◽  
pp. 1650017
Author(s):  
Jianhua Tang ◽  
Linfang Qian ◽  
Qiang Yin
Keyword(s):  
Numerical Integration ◽  
Fourth Order ◽  
Integration Method ◽  
Dynamic Equations ◽  
Reconstruction Method ◽  
Order Accuracy ◽  
Runge Kutta ◽  
Multi Body ◽  
Different Order ◽  
Body Dynamic

Commutator free method is an effective method for solving rotating integration. Numerical examples show that the use of the proposed combining method can achieve the same order accuracy with less computation than other geometry integration method. However, it is difficult to be directly applied to mechanic dynamics solutions. In this paper, commutator free method which is often applied to rotation integration and classical Runge–Kutta (RK) method which is usually operated in Linear space are combined to solve the multi-body dynamic equations. The explicit Runge–Kutta coefficients are reconstructed to meet different order accuracy integration methods. The reconstruction method is discussed and coefficients are given. With this method, the dynamic equations can be solved accurately and economically without much modification on the classical numerical integration. Moreover, CG method and CF method can also be combined with adaptive RK method without many changes. Finally, the results of the examples show that with less computation, fourth-order combining method is as accurate as fourth-order Crouch–Grossman algorithm.

scholarly journals Nonoscillatory solutions to fourth-order neutral dynamic equations on time scales

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yang-Cong Qiu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Fourth Order ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Nonoscillatory Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations

AbstractIn this paper, we present some sufficient conditions and necessary conditions for the existence of nonoscillatory solutions to a class of fourth-order nonlinear neutral dynamic equations on time scales by employing Banach spaces and Krasnoselskii’s fixed point theorem. Two examples are given to illustrate the applications of the results.

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