Oscillatory behavior of the second-order nonlinear neutral difference equations

2001 ◽  
Vol 8 (1) ◽  
pp. 111-128
Author(s):  
Zhenguo Zhang ◽  
Wenlei Dong ◽  
Bi Ping
Keyword(s):  
Difference Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Difference Equations

scholarly journals Oscillatory behavior of second order unstable type neutral difference equations

2005 ◽  
Vol 36 (1) ◽  
pp. 57-68
Author(s):  
E. Thandapani ◽  
S. Pandian ◽  
R. K. Balasubramanian
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Difference Equations ◽  
Neutral Type ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Difference Equations ◽  
Unbounded Solutions ◽  
Unstable Type ◽  
Positive Integers

This paper deals with the oscillatory behavior of all bounded/ unbounded solutions of second order neutral type difference equation of the form$$ \Delta (a_n(\Delta_c y_n+py_{n-k}))^\alpha)-g_nf(y_{\sigma(n)})=0, $$where $ p $ is real, $ \alpha $ is a ratio of odd positive integers, $ k $ is a positive integer and $ \{\sigma(n)\} $ is a sequence of integers. Examples are provided to illustrate the results.

MODIFIED OSCILLATION CRITERIA OF SECOND-ORDER NEUTRAL DIFFERENCE EQUATIONS

2021 ◽  
Vol 28 (1-2) ◽  
pp. 19-30
Author(s):  
G. CHATZARAKIS G. CHATZARAKIS ◽  
R. KANAGASABAPATHI R. KANAGASABAPATHI ◽  
S. SELVARANGAM S. SELVARANGAM ◽  
E. THANDAPANI E. THANDAPANI
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Nonlinear Difference Equations ◽  
Transformation Technique ◽  
Neutral Difference Equations ◽  
Oscillation Criteria ◽  
Neutral Term

In this paper we shall consider a class of second-order nonlinear difference equations with a negative neutral term. Some new oscillation criteria are obtained via Riccati transformation technique. These criteria improve and modify the existing results mentioned in the literature. Some examples are given to show the applicability and significance of the main results.

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