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Global attractivity for a nonlinear difference equation with variable delay

✍ Scribed by H. Matsunaga; T. Hara; S. Sakata

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
358 KB
Volume
41
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper, we give sufficient conditions under which every solution of the nonlinear difference equation with variable delay

tends to zero as n --+ c<). Here, {Pn} is a nonnegative sequence, f : R --+ R is a continuous function with xf(x) > 0 if x ~ 0, and g : N --~ Z is nondecreasing and satisfies g(n) < n for n >_ 0 and limn-~co g(n) --oo. (~) 2001 Elsevier Science Ltd. All rights reserved. ieywords--Nonlinear difference equation with delay, Global attractivity.

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Consider the nonautonomous delay logistic difference equation /kyn=pnyn(1--Yn~k'-"--~"), n=0,1 ..... (1.1) where {Pn}n>\_o is a sequence of nonnegative real numbers, {kn}n>\_o is a sequence of positive integers, {n -kn) is nondecreasing, limn--.co(n -kn) --vo, and ,k is a positive constant. We obta