scholarly journals Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shanliang Zhu ◽  
Chunyun Sheng
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation

scholarly journals On Inequalities of Lyapunov for Two-Dimensional Nonlinear Dynamic Systems on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Qiao-Luan Li ◽  
Wing-Sum Cheung ◽  
Xu-Yang Fu
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Type Equation ◽  
Nonlinear Dynamic Systems ◽  
Two Dimensional

We establish some new Lyapunov-type inequalities for two-dimensional nonlinear dynamic systems on time scales. As for application, boundedness of the Emden-Fowler-type equation is proved.

Higher order nonlinear dynamic systems on time scales

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Mustafa Günendi ◽  
İsmail Yaslan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Existence Of Solutions ◽  
Higher Order ◽  
Nonlinear Dynamic Systems ◽  
Point Boundary

AbstractIn this paper, we consider a nonlinear system of higher order three-point boundary value problems on time scales. The Schauder fixed point theorem is used to investigate the existence of solutions of nonlinear dynamic systems on time scales. Furthermore, we establish the criteria for the existence of at least one, two and three positive solutions for higher order nonlinear dynamic systems on time scales by using the four functionals fixed point theorem, the Avery–Henderson fixed point theorem and the five functionals fixed point theorem, respectively.

scholarly journals A new oscillation criterion for two-dimensional dynamic systems on time scales

2011 ◽  
Vol 42 (2) ◽  
pp. 237-244
Author(s):  
Jia Baoguo
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Continuous Functions ◽  
Oscillation Criterion ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
And Mathematics ◽  
Computers And Mathematics ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation

Consider the linear dynamic system on time scales\begin{equation}u^\Delta=pv, \quad\quad v^\Delta=-qu^\sigma\end{equation}where $p>0$ and $q$ are rd-continuous functions on a time scale $\mathbb T$ such that $\sup\mathbb T=\infty$. When $p(t)$ is allowed to take on negative values, we establish an oscillation criterion for system (0.1). Our result improves a main result of Fu and Lin [S. C. Fu and M. L. Lin, Oscillation and nonoscillation criteria for linear dynamic systems on time scales, Computers and Mathematics with Applications, 59(2010), 2552-2565].

Sign in / Sign up

Export Citation Format

Share Document