scholarly journals Frequent Oscillation Criteria for a Delay Difference Equation

2003 ◽  
Vol 46 (3) ◽  
pp. 421-439
Author(s):  
Chuan-Jun TIAN ◽  
Sui Sun CHENG ◽  
Sheng-Li XIE
Keyword(s):  
Difference Equation ◽  
Delay Difference Equation ◽  
Oscillation Criteria ◽  
Delay Difference ◽  
Frequent Oscillation

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.

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.

Improved oscillation criteria for second order nonlinear delay difference equations with non-positive neutral term

2016 ◽  
Vol 56 (1) ◽  
pp. 155-165 ◽  
Author(s):  
E. Thandapani ◽  
S. Selvarangam ◽  
R. Rama ◽  
M. Madhan
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Second Order ◽  
Delay Difference Equation ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Positive Integers ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

Abstract In this paper, we present some oscillation criteria for second order nonlinear delay difference equation with non-positive neutral term of the form $$\Delta (a_n (\Delta z_n )^\alpha ) + q_n f(x_{n - \sigma } ) = 0,\;\;\;n \ge n_0 > 0,$$ where zn = xn − pnxn−τ, and α is a ratio of odd positive integers. Examples are provided to illustrate the results. The results obtained in this paper improve and complement to some of the existing results.

scholarly journals Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
G. M. Moremedi ◽  
I. P. Stavroulakis
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Difference Equations ◽  
Delay Difference Equation ◽  
Real Numbers ◽  
First Order ◽  
All Solutions ◽  
Delay Difference ◽  
Constant Argument

Consider the first-order delay difference equation with a constant argument Δxn+pnxn-k=0,  n=0,1,2,…, and the delay difference equation with a variable argument Δxn+pnxτn=0,  n=0,1,2,…, where p(n) is a sequence of nonnegative real numbers, k is a positive integer, Δx(n)=x(n+1)-x(n), and τ(n) is a sequence of integers such that τ(n)≤n-1 for all n≥0 and limn→∞τ(n)=∞. A survey on the oscillation of all solutions to these equations is presented. Examples illustrating the results are given.

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