Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations

2000 ◽  
Vol 19 (3) ◽  
pp. 863-872 ◽  
Author(s):  
E. Thandapani ◽  
I.M. Arockiasamy
2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yuhua Long ◽  
Shaohong Wang ◽  
Jiali Chen

Abstract In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.


2019 ◽  
Vol 110 (1) ◽  
pp. 165-197
Author(s):  
M. Folly-Gbetoula ◽  
D. Nyirenda

2015 ◽  
Vol 46 (4) ◽  
pp. 441-451 ◽  
Author(s):  
Ethiraju Thandapani ◽  
Devarajulu Seghar ◽  
Sandra Pinelas

In this paper we obtain some new oscillation criteria for the neutral difference equation \begin{equation*} \Delta \Big(a_n (\Delta (x_n-p_n x_{n-k}))\Big)+q_n f(x_{n-l})=0 \end{equation*} where $0\leq p_n\leq p0$ and $l$ and $k$ are positive integers. Examples are presented to illustrate the main results. The results obtained in this paper improve and complement to the existing results.


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