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.

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 of nonlinear neutral dynamic equations on time scales

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
G. N. Chhatria ◽  
Said R. Grace ◽  
John R. Graef
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Nonlinear Function ◽  
Dynamic Equations ◽  
Krasnosel’Skii’S Fixed Point Theorem ◽  
Necessary And Sufficient ◽  
Strongly Sublinear ◽  
Neutral Dynamic Equations

AbstractThe authors present necessary and sufficient conditions for the oscillation of a class of second order non-linear neutral dynamic equations with non-positive neutral coefficients by using Krasnosel’skii’s fixed point theorem on time scales. The nonlinear function may be strongly sublinear or strongly superlinear.

scholarly journals Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale

2018 ◽  
Vol 36 (2) ◽  
pp. 185
Author(s):  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scale ◽  
Variable Coefficients ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations ◽  
Compact Map

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan <cite>c1</cite>.

scholarly journals Multiple Positive Symmetric Solutions top-Laplacian Dynamic Equations on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-27
Author(s):  
You-Hui Su ◽  
Can-Yun Huang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Discrete Equations ◽  
Special Cases ◽  
Krasnosel’Skii’S Fixed Point Theorem

This paper makes a study on the existence of positive solution top-Laplacian dynamic equations on time scales&#x1D54B;. Some new sufficient conditions are obtained for the existence of at least single or twin positive solutions by using Krasnosel'skii's fixed point theorem and new sufficient conditions are also obtained for the existence of at least triple or arbitrary odd number positive solutions by using generalized Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem. As applications, two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.

scholarly journals Nonoscillatory Solutions for System of Neutral Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Zhanhe Chen ◽  
Taixiang Sun ◽  
Qi Wang ◽  
Hongjian Xi
Keyword(s):  
Time Scales ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Functional System ◽  
Dynamic Equations ◽  
Nonoscillatory Solutions ◽  
Neutral Dynamic Equations

We will discuss nonoscillatory solutions to then-dimensional functional system of neutral type dynamic equations on time scales. We will establish some sufficient conditions for nonoscillatory solutions with the propertylimt→∞⁡xit=0, i=1, 2, …,n.

scholarly journals Existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales

2021 ◽  
Vol 7 (1) ◽  
pp. 20-29
Author(s):  
Faycal Bouchelaghem ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Main Tool ◽  
Second Order ◽  
Dynamic Equations ◽  
Existence Of Positive Solutions ◽  
Neutral Dynamic Equations

AbstractIn this article we study the existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales. The main tool employed here is Schauder’s fixed point theorem. The results obtained here extend the work of Culakova, Hanustiakova and Olach [12]. Two examples are also given to illustrate this work.

Periodic Solutions of Almost Linear Volterra Integro-dynamic Equations on Periodic Time Scales

2015 ◽  
Vol 58 (1) ◽  
pp. 174-181 ◽  
Author(s):  
Youssef N. Raffoul
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Discrete Time ◽  
Dynamic Equations ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Periodic Solutions

AbstractUsing Krasnoselskii’s fixed point theorem, we deduce the existence of periodic solutions of nonlinear system of integro-dynamic equations on periodic time scales. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. The results of this paper are new for the continuous and discrete time scales.

scholarly journals Existence of Positive Solutions for Fourth-Order Boundary Value Problems with Sign-Changing Nonlinear Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xingfang Feng ◽  
Hanying Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions

the existence of positive solutions for a fourth-order boundary value problem with a sign-changing nonlinear term is investigated. By using Krasnoselskii’s fixed point theorem, sufficient conditions that guarantee the existence of at least one positive solution are obtained. An example is presented to illustrate the application of our main results.

On oscillatory and asymptotic behavior of fourth order nonlinear neutral delay dynamic equations with positive and negative coefficients

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
John Graef ◽  
Saroj Panigrahi ◽  
P. Reddy
Keyword(s):  
Fixed Point ◽  
Fourth Order ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Positive And Negative Coefficients ◽  
Delay Dynamic Equations ◽  
Krasnosel’Skii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations

AbstractIn this paper, oscillatory and asymptotic properties of solutions of nonlinear fourth order neutral dynamic equations of the form $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = 0(H)$ and $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = f(t),(NH)$ are studied on a time scale $\mathbb{T}$ under the assumption that $\int\limits_{t_0 }^\infty {\tfrac{t} {{r(t)}}\Delta t = \infty } $ and for various ranges of p(t). In addition, sufficient conditions are obtained for the existence of bounded positive solutions of the equation (NH) by using Krasnosel’skii’s fixed point theorem.

scholarly journals Nonoscillatory Solutions for Higher-Order Neutral Dynamic Equations on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Taixiang Sun ◽  
Hongjian Xi ◽  
Xiaofeng Peng ◽  
Weiyong Yu
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Dynamic Equations ◽  
Bounded Solutions ◽  
Nonoscillatory Solutions ◽  
Neutral Dynamic Equation ◽  
Necessary And Sufficient ◽  
Neutral Dynamic Equations

We study the higher-order neutral dynamic equation{a(t)[(x(t)−p(t)x(τ(t)))Δm]α}Δ+f(t,x(δ(t)))=0fort∈[t0,∞)Tand obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.

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