riccati techniques
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We discuss the discrete Oscillatory properties of Fourth order non linear difference equation. whereα >1. In particular we establish the discrete oscillation using Riccati Techniques and Conjugacy criteria. The Proofs of all the results in this paper are based on the Riccati technique.


2016 ◽  
Vol 14 (1) ◽  
pp. 497-508 ◽  
Author(s):  
Jessada Tariboon ◽  
Sotiris K. Ntouyas

AbstractIn this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form$$\left\{ \begin{array}{l} {t_k}{D^\alpha }\left( {p\left( t \right)\left[ {{t_k}{D^\alpha }x\left( t \right) + r\left( t \right)x\left( t \right)} \right]} \right) + q\left( t \right)x\left( t \right) = 0,\quad t \ge {t_0},\;t \ne {t_k},\\ x\left( {t_k^ + } \right) = {a_k}x(t_k^ - ),\quad {t_k}{D^\alpha }x\left( {t_k^ + } \right) = {b_{k\;{t_{k - 1}}}}{D^\alpha }x(t_k^ - ),\quad \;k = 1,2, \ldots. \end{array} \right.$$Some new oscillation results are obtained by using the equivalence transformation and the associated Riccati techniques.


2009 ◽  
Vol 58 (6) ◽  
pp. 1211-1222 ◽  
Author(s):  
Qi-Ru Wang ◽  
Yuan-Tong Xu ◽  
Ronald M. Mathsen

1994 ◽  
Vol 25 (4) ◽  
pp. 343-352
Author(s):  
B. G. ZHANG ◽  
PENGXIANG YAN

In this paper we study qualitative properties of solutions of the neutral difference equation $$ \Delta(y_n-py_{n-k})+\sum_{i=1}^m q_n^i y_{n-k_i} =0 $$ $$ y_n=A_n \quad \text{ for } n=-M, \cdots, -1, 0$$ where $p \ge 1$, $M =\max\{k, k_1, \cdots, k_m\}$, and $k$, $k_i$, $i =1, \cdots, m$, are nonnegative integers. Riccati techniques are used.  


1989 ◽  
Vol 142 (2) ◽  
pp. 468-487 ◽  
Author(s):  
Shaozhu Chen ◽  
Lynn H Erbe
Keyword(s):  

1988 ◽  
Vol 33 (4) ◽  
pp. 379-381 ◽  
Author(s):  
M.-A. Poubelle ◽  
R.R. Bitmead ◽  
M.R. Gevers
Keyword(s):  

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