Publications (14)6.34 Total impact
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ABSTRACT: In this paper, we consider higher order nonlinear neutral dynamic equations on time scales. Some sufficient conditions are obtained for existence of positive solutions for the higher order equations by using the fixed point theory and defining the compressed map on a set.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we investigate the oscillation of Thirdorder difference equation with impulses. Some sufficient conditions for the oscillatory behavior of the solutions of Thirdorder impulsive difference equations are obtained.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we consider the higherorder nonlinear neutral delay differential equation (1.1)(x(t)−p(t)x(t−τ))(n)+f(t,x(σ(t)))=0 where n is an odd number and n⩾3,τ>0, p,σ∈C([t0,∞),R+),σ(t)⩽t,limt→∞σ(t)=∞, f∈C([t0,∞)×R,R),f(t,u) is nondecreasing in u. 
Article: Existence of nonoscillatory solutions for higher order neutral dynamic equations on time scales
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ABSTRACT: In this paper, we consider higher order nonlinear neutral dynamic equation on time scales. Some sufficient conditions are obtained for existence of a nonoscillatory solution for the higher order equation by using fixed point theory and defining the compressed injection on a set.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we investigate nonoscillatory solutions of a class of higher order neutral nonlinear difference equations with positive and negative coefficients . Some sufficient conditions for the existence of nonoscillatory solutions are obtained. 
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ABSTRACT: In this paper, we investigate the oscillation of secondorder selfconjugate differential equation with impulses(1)(a (t) (x (t) + p (t) x (t  τ))′)′ + q (t) x (t  σ) = 0, t ≠ tk, t ≥ t0,(2)x (tk+) = (1 + bk) x (tk), k = 1, 2, ...,(3)x′ (tk+) = (1 + bk) x′ (tk), k = 1, 2, ...,where a, p, q are continuous functions in [t0, + ∞), q (t) ≥ 0, a (t) > 0, ∫t0∞ (1 / a (s)) d s = ∞, τ > 0, σ > 0, bk >  1,0 < t0 < t1< t2 < ⋯ < tk < ⋯ and limk → ∞ tk = ∞. We get some sufficient conditions for the oscillation of solutions of Eqs. (1)(3).  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we consider the oscillation of first order sublinear difference equation with positive neutral termΔ(x(n) + p(n)x(τ(n))) + f(n, x(g1(n)), ... ,x(gm(n))) = 0. We obtain necessary and sufficient conditions for the solutions of this equation to be oscillatory. 

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ABSTRACT: We investigate the oscillation of a secondorder nonlinear differential equation of the form y (t) + p (t) y τ ( t ) '' +ft , y g ( t )=e(t),t≥t 0 , where p,τ,e∈C(I,ℝ), g∈C 1 (I,ℝ), I=[t 0 ,∞), lim t→∞ p(t)=p, τ(t), g(t)≤t, lim t→∞ τ(t)=∞, and lim t→∞ g(t)=∞. There exists a function r∈C 2 (I,ℝ) such that e(t)=r '' (t) and r changes sign on [T,∞) for any T≥t 0 , f∈C(I×ℝ,ℝ), f(t,y)sgny≥q(t)y or f(t,y)=q(t)f 1 (y). By using the generalized Riccati technique and averaging technique, we get some new oscillation criteria. 

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ABSTRACT: In this paper, we are mainly concerned with the classification of nonoscillatory solutions for the higher order difference equation and some existence results for some kinds of nonoscillatory solutions.
Publication Stats
32  Citations  
6.34  Total Impact Points  
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20012009

Hebei Normal University
 College of Mathematics and Information Science
Chentow, Hebei, China
