scholarly journals Existence of the nonoscillatory solutions of higher order neutral dynamic equations on time scales

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Chunyan Tao ◽  
Taixiang Sun ◽  
Hongjian Xi
2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Taixiang Sun ◽  
Hongjian Xi ◽  
Xiaofeng Peng ◽  
Weiyong Yu

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.


2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yong Zhou ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad

Abstract We present the oscillation criteria for the following neutral dynamic equation on time scales: $$ \bigl(y(t)-C(t)y(t-\zeta )\bigr)^{\Delta }+P(t)y(t-\eta )-Q(t)y(t-\delta )=0, \quad t\in {\mathbb{T}}, $$ ( y ( t ) − C ( t ) y ( t − ζ ) ) Δ + P ( t ) y ( t − η ) − Q ( t ) y ( t − δ ) = 0 , t ∈ T , where $C, P, Q\in C_{\mathit{rd}}([t_{0},\infty ),{\mathbb{R}}^{+})$ C , P , Q ∈ C rd ( [ t 0 , ∞ ) , R + ) , ${\mathbb{R}} ^{+}=[0,\infty )$ R + = [ 0 , ∞ ) , $\gamma , \eta , \delta \in {\mathbb{T}}$ γ , η , δ ∈ T and $\gamma >0$ γ > 0 , $\eta >\delta \geq 0$ η > δ ≥ 0 . New conditions for the existence of nonoscillatory solutions of the given equation are also obtained.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yang-Cong Qiu

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Zhanhe Chen ◽  
Taixiang Sun ◽  
Qi Wang ◽  
Hongjian Xi

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.


2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yang-Cong Qiu

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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