scholarly journals Oscillation for nonlinear delay difference equations

2001 ◽  
Vol 32 (4) ◽  
pp. 275-280 ◽  
Author(s):  
X. H. Tang
Keyword(s):  
Oscillatory Behavior ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Delay Difference Equation ◽  
First Order ◽  
Condition Of Oscillation ◽  
Necessary And Sufficient ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

The oscillatory behavior of the first order nonlinear delay difference equation of the form $$ x_{n+1} - x_n + p_n x_{n-k}^{\alpha} = 0, ~~~ n = 0, 1, 2, \ldots ~~~~~~~ \eqno{(*)} $$ is investigated. A necessary and sufficient condition of oscillation for sublinear equation (*) ($ 0 < \alpha < 1 $) and an almost sharp sufficient condition of oscillation for superlinear equation (*) ($ \alpha > 1 $) are obtained.

scholarly journals Necessary and sufficient conditions for oscillation of first order neutral delay difference equations

2015 ◽  
Vol 3 (2) ◽  
pp. 61
Author(s):  
A. Murgesan ◽  
P. Sowmiya
Keyword(s):  
Difference Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
First Order ◽  
Constant Coefficients ◽  
Necessary And Sufficient ◽  
Delay Difference Equations ◽  
Delay Difference

<p>In this paper, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the first order neutral delay difference equation with constant coefficients of the form <br />\begin{equation*} \quad \quad \quad \quad \Delta[x(n)-px(n-\tau)]+qx(n-\sigma)=0, \quad \quad n\geq n_0 \quad \quad \quad \quad \quad \quad {(*)} \end{equation*}<br />by constructing several suitable auxiliary functions. Some examples are also given to illustrate our results.</p>

scholarly journals Some New Oscillation Criteria for Fourth-Order Nonlinear Delay Difference Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kandasamy Alagesan ◽  
Subaramaniyam Jaikumar ◽  
Govindasamy Ayyappan
Keyword(s):  
Difference Equation ◽  
Fourth Order ◽  
Difference Equations ◽  
Oscillatory Behavior ◽  
Delay Difference Equation ◽  
Oscillation Criteria ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

In this paper, the authors studied oscillatory behavior of solutions of fourth-order delay difference equation Δc3nΔc2nΔc1nΔun+pnfun−k=0 under the conditions ∑n=n0∞cin<∞, i=1, 2, 3. New oscillation criteria have been obtained which greatly reduce the number of conditions required for the studied equation. Some examples are presented to show the strength and applicability of the main results.

scholarly journals Existence of nonoscillatory solutions of first order nonlinear neutral equations

1990 ◽  
Vol 32 (2) ◽  
pp. 180-192 ◽  
Author(s):  
Lu Wudu
Keyword(s):  
Nonoscillatory Solution ◽  
Sufficient Condition ◽  
Neutral Equation ◽  
Necessary And Sufficient Condition ◽  
Nonoscillatory Solutions ◽  
Neutral Equations ◽  
First Order ◽  
Image Position ◽  
Necessary And Sufficient

AbstractConsider the nonlinear neutral equationwhere pi(t), hi(t), gj(t), Q(t) Є C[t0, ∞), limt→∞hi(t) = ∞, limt→∞gj(t) = ∞ i Є Im = {1, 2, …, m}, j Є In = {1, 2, …, n}. We obtain a necessary and sufficient condition (2) for this equation to have a nonoscillatory solution x(t) with limt→∞ inf|x(t)| > 0 (Theorems 5 and 6) or to have a bounded nonoscillatory solution x(t) with limt→∞ inf|x(t)| > 0 (Theorem 7).

scholarly journals On B- Covariant Derivative of First Order for Some Tensors in different Spaces

2021 ◽  
Vol 2 (2) ◽  
pp. 30-37
Author(s):  
Alaa A. Abdallah ◽  
A. A. Navlekar ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Torsion Tensor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Recurrence Property ◽  
Necessary And Sufficient ◽  
The Relationship

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

A Necessary and Sufficient Condition for the Oscillation of an Even Order Nonlinear Delay Differential Equation

1973 ◽  
Vol 25 (5) ◽  
pp. 1078-1089 ◽  
Author(s):  
Bhagat Singh
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Oscillatory Behavior ◽  
Necessary And Sufficient Condition ◽  
Even Order ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

In this paper we study the oscillatory behavior of the even order nonlinear delay differential equation(1)where(i) denotes the order of differentiation with respect to t. The delay terms τi σi are assumed to be real-valued, continuous, non-negative, non-decreasing and bounded by a common constant M on the half line (t0, + ∞ ) for some t0 ≧ 0.

scholarly journals Oscillatory and Asymptotic Behavior of a First-Order Neutral Equation of Discrete Type with Variable Several Delay under Δ Sign

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Radhanath Rath ◽  
Chittaranjan Behera
Keyword(s):  
Difference Operator ◽  
Sufficient Conditions ◽  
Neutral Equation ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
First Order ◽  
Forward Difference ◽  
Necessary And Sufficient ◽  
Positive Integers ◽  
Delay Difference

We obtain necessary and sufficient conditions so that every solution of neutral delay difference equation Δyn-∑j=1kpnjyn-mj+qnG(yσ(n))=fn oscillates or tends to zero as n→∞, where {qn} and {fn} are real sequences and G∈C(R,R), xG(x)>0, and m1,m2,…,mk are positive integers. Here Δ is the forward difference operator given by Δxn=xn+1-xn, and {σn} is an increasing unbounded sequences with σn≤n. This paper complements, improves, and generalizes some past and recent results.

scholarly journals Oscillation of nonlinear delay difference equations

2001 ◽  
Vol 28 (5) ◽  
pp. 301-306 ◽  
Author(s):  
Jianchu Jiang
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Delay Difference Equation ◽  
Oscillation Criteria ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

We obtain some oscillation criteria for solutions of the nonlinear delay difference equation of the formxn+1−xn+pn∏j=1mxn−kjαj=0.

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