Property B of the Four-Dimensional Neutral Difference System

2017 ◽  
pp. 147-163
Author(s):  
Jana Krejčová
Keyword(s):  
Difference System ◽  
Property B

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.

scholarly journals Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui-Sheng Ding ◽  
Julio G. Dix
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Type System ◽  
Functional Difference ◽  
Difference System ◽  
Multiple Periodic Solutions

This paper is concerned with the existence of multiple periodic solutions for discrete Nicholson’s blowflies type system. By using the Leggett-Williams fixed point theorem, we obtain the existence of three nonnegative periodic solutions for discrete Nicholson’s blowflies type system. In order to show that, we first establish the existence of three nonnegative periodic solutions for then-dimensional functional difference systemyk+1=Akyk+fk, yk-τ, k∈ℤ, whereAkis not assumed to be diagonal as in some earlier results. In addition, a concrete example is also given to illustrate our results.

scholarly journals On the oscillation of a nonlinear two-dimensional difference systems

2001 ◽  
Vol 32 (3) ◽  
pp. 201-209 ◽  
Author(s):  
E. Thandapani ◽  
B. Ponnammal
Keyword(s):  
Asymptotic Behavior ◽  
Sufficient Conditions ◽  
Real Sequence ◽  
Two Dimensional ◽  
Difference System ◽  
Nonoscillatory Solutions ◽  
Difference Systems ◽  
All Solutions ◽  
Necessary And Sufficient ◽  
Strongly Sublinear

The authors consider the two-dimensional difference system$$ \Delta x_n = b_n g (y_n) $$ $$ \Delta y_n = -f(n, x_{n+1}) $$where $ n \in N(n_0) = \{ n_0, n_0+1, \ldots \} $, $ n_0 $ a nonnegative integer; $ \{ b_n \} $ is a real sequence, $ f: N(n_0) \times {\rm R} \to {\rm R} $ is continuous with $ u f(n,u) > 0 $ for all $ u \ne 0 $. Necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior are given. Also sufficient conditions for all solutions to be oscillatory are obtained if $ f $ is either strongly sublinear or strongly superlinear. Examples of their results are also inserted.

On Property B of Families of Sets

1980 ◽  
Vol 23 (4) ◽  
pp. 429-435 ◽  
Author(s):  
H. L. Abbott ◽  
A. C. Liu
Keyword(s):  
Property B

A family of sets is said to have property B if there exists a set S such that S∩F≠ ϕ and SF for all F . S is called a B-set for . Let n≥2 and N≥2n-1. Let V = { 1, 2,≠, N} and let = {G:G⊂ V, |G| = rc}. Erdös [3] defined mN(n) to be the size of a smallest subfamily of which does not have property B and proved the following results:

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