scholarly journals Existence of nonoscillatory solutions for system of neutral difference equations

2015 ◽  
Vol 9 (2) ◽  
pp. 271-284 ◽  
Author(s):  
Małgorzata Migda ◽  
Ewa Schmeidel ◽  
Małgorzata Zdanowicz
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Neutral Difference Equations

The system of neutral type difference equations with delays {?(x(n) + p(n) x(n - ?))= a(n) f(y(n - l)) ?y(n) = b(n) g(z(n - m)) ?z(n) = c(n) h(x(n - k)) is considered. The aim of this paper is to present sufficient conditions for the existence of nonoscillatory bounded positive solutions of the considered system with various (p(n)).

scholarly journals Neutral Difference System and its Nonoscillatory Solutions

2018 ◽  
Vol 71 (1) ◽  
pp. 139-148
Author(s):  
Jana Pasáčková
Keyword(s):  
Difference Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Difference System ◽  
Nonlinear Difference Equations ◽  
Nonoscillatory Solutions ◽  
Weak Property ◽  
Property B

Abstract The paper deals with a system of four nonlinear difference equations where the first equation is of a neutral type. We study nonoscillatory solutions of the system and we present sufficient conditions for the system to have weak property B.

Oscillation of fourth order nonlinear neutral difference equations I

2008 ◽  
Vol 58 (2) ◽  
Author(s):  
A. Tripathy
Keyword(s):  
Asymptotic Behaviour ◽  
Positive Solutions ◽  
Fourth Order ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Neutral Difference Equations ◽  
Asymptotic Behaviour Of Solutions

AbstractOscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral difference equations of the form $$ \Delta ^2 (r(n)\Delta ^2 (y(n) + p(n)y(n - m))) + q(n)G(y(n - k)) = 0 $$ and $$ (NH) \Delta ^2 (r(n)\Delta ^2 (y(n) + p(n)y(n - m))) + q(n)G(y(n - k)) = f(n) $$ are studied under the assumption $$ \sum\limits_{n = 0}^\infty {\tfrac{n} {{r(n)}} = \infty } $$, for various ranges of p(n). Sufficient conditions are obtained for the existence of bounded positive solutions of (NH).

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 $c =1$.

scholarly journals Existence of Nonoscillatory Solutions of First-Order Neutral Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Božena Dorociaková ◽  
Anna Najmanová ◽  
Rudolf Olach
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Existence Of Positive Solutions ◽  
Positive Functions ◽  
Bounded Below

This paper contains some sufficient conditions for the existence of positive solutions which are bounded below and above by positive functions for the first-order nonlinear neutral differential equations. These equations can also support the existence of positive solutions approaching zero at infinity

scholarly journals Existence of nonoscillatory solutions to third order nonlinear neutral difference equations

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4981-4991
Author(s):  
K.S. Vidhyaa ◽  
C. Dharuman ◽  
John Graef ◽  
E. Thandapani
Keyword(s):  
Fixed Point ◽  
Sufficient Conditions ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Neutral Difference Equations ◽  
Positive And Negative Coefficients ◽  
The Third ◽  
Delay Difference

The authors consider the third order neutral delay difference equation with positive and negative coefficients ?(an?(bn?(xn + pxn-m)))+pnf(xn-k)- qn1(xn-l) = 0, n ? n0, and give some new sufficient conditions for the existence of nonoscillatory solutions. Banach?s fixed point theorem plays a major role in the proofs. Examples are provided to illustrate their main results.

scholarly journals Existence of positive solutions for certain partial difference equations

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
Binggen Zhang ◽  
Qiuju Xing
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Partial Difference Equation ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Existence Of Positive Solutions

We give some sufficient conditions for the existence of positive solutions of partial difference equationaAm+1,n+1+bAm,n+1+cAm+1,n−dAm,n+Pm,nAm−k,n−1=0by two different methods.

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