Classifications and existence of positive solutions of higher-order nonlinear neutral difference equations

2004 ◽  
Vol 152 (2) ◽  
pp. 351-366 ◽  
Author(s):  
Wan-Tong Li
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
Higher Order ◽  
Neutral Difference Equations ◽  
Existence Of Positive Solutions

scholarly journals ON EXISTENCE OF POSITIVE SOLUTIONS OF NEUTRAL DIFFERENCE EQUATIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 257-265
Author(s):  
J. H. SHEN ◽  
Z. C. WANG ◽  
X. Z. QIAN
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Positive Solution ◽  
Positive Solutions ◽  
Difference Equations ◽  
Real Numbers ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Existence Of Positive Solutions

Consider the neutral difference equation \[\Delta(x_n- cx_{n-m})+p_nx_{n-k}=0, n\ge N\qquad (*) \] where $c$ and $p_n$ are real numbers, $k$ and $N$ are nonnegative integers, and $m$ is positive integer. We show that if \[\sum_{n=N}^\infty |p_n|<\infty \qquad (**) \] then Eq.(*) has a positive solution when $c \neq 1$. However, an interesting example is also given which shows that (**) does not imply that (*) has a positive solution when $c =1$.

Existence of Positive Solutions for a Class of Higher-Order Neutral Delay Difference Equations

2011 ◽  
Vol 50-51 ◽  
pp. 761-765
Author(s):  
Dong Hua Wang ◽  
Yu Huan Cui ◽  
Pu Yu Hao
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Higher Order ◽  
Sufficient Condition ◽  
Neutral Delay ◽  
Existence Of Positive Solutions ◽  
Delay Difference Equations ◽  
Delay Difference

In this paper, a class of higher-order neutral delay difference equations is investigated. Some sufficient condition of the asymptotic behavior and existence of positive solutions for the equations are obtained. At last, we give their applications to some more general equations.

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