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Page 7797 of Mathematical Reviews Vol. , Issue 98M
[page]

1998
*
Mathematical Reviews
*

Yu, “A

*necessary**and**sufficient**condition**and*its applications*for*the global asymptotic*stability**of*zero solution in a delay*difference**equation*”, Acta Math. ... Summary: “In this paper, some*sufficient**conditions*are obtained*for*the global asymptotic*stability**of*a nonlinear nonautonomous*difference**equation*with delays*and*the results in papers by I. ...##
###
Page 5762 of Mathematical Reviews Vol. , Issue 2002H
[page]

2002
*
Mathematical Reviews
*

*Necessary*

*and*

*sufficient*

*conditions*

*for*the existence

*of*nonoscillatory solutions with a specified asymptotic behavior,

*and*

*sufficient*

*conditions*

*for*all solutions to be oscillatory if f is either strongly ... The authors are interested in proving

*necessary*

*and*

*sufficient*con- ditions

*for*oscillations

*of*hyperbolic

*and*elliptic type partial

*differ*- ence

*equations*. ...

##
###
Dynamics of the equation in the complex plane

2015
*
Cogent Mathematics
*

We investigate the dynamics

doi:10.1080/23311835.2015.1122276
fatcat:r4ueadp3xbbkvg76czbsfmiism
*of*the second-*order*rational*difference**equation*in the title with complex parameters*and*arbitrary complex initial*conditions*. ... Analysis*of*the local*stability**of*the equilibria*and*periodicity*of*solutions has been carried out. ... It will provide*necessary**and**sufficient**conditions**for*local asymptotic*stability**of*the equilibria. ...##
###
Page 7092 of Mathematical Reviews Vol. , Issue 2000j
[page]

2000
*
Mathematical Reviews
*

The authors give

*necessary**and**sufficient**conditions**for*{R,(x)} to satisfy the second-*order**differ*- ence*equation*/)(x)AVy(x) +/(x)Ay(x) = Any(x), where (x) = lx? ...*of**stability**and**boundedness*with respect to partial components*for*finite delay*difference*systems. ...##
###
Page 8673 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

Summary: “Several

*necessary**and*/or*sufficient**conditions*are given*for*the existence*of*unbounded positive solutions*of*non- linear*difference**equations**of*the form A”x,_; +*of*(*n*, X,_1) = 0,*n*€ No, where ...*Necessary**and**sufficient**conditions**for**boundedness*, persistence,*and*periodicity*of*all solutions are established. The oscillatory behavior is investigated.” ...##
###
Page 229 of Mathematical Reviews Vol. , Issue 94a
[page]

1994
*
Mathematical Reviews
*

229 34K Functional-differential

*and*differential-*difference**equations*94a:34106 34K15 92D40 Yang, Zheng Qing (PRC-SCN; Guangzhou)*Necessary**and**sufficient**conditions**for*oscillation*of*delay-logistic*equations*... The author is searching*for**necessary**and**sufficient**conditions**for*uniform*boundedness**of*the solutions*and*their derivatives on [0,00), or the global asymptotic*stability**of*the zero solution in the ...##
###
Page 8022 of Mathematical Reviews Vol. , Issue 2001K
[page]

2001
*
Mathematical Reviews
*

A

*necessary**and**sufficient**condition**for*the periodicity*of*the generalized Lyness*equation*a ———. =@,1,2.-:-, (a +bxn)Xn—1 Rm Xn+1 = is given*and*a*sufficient**condition**for*the strict oscillation*of*all ...*Stability**and**boundedness**of*solutions are studied*for*the finite delay*difference*system (el) x(*n*+1) = f(*n*,x,),*n*€ Z*, where f:Z*+ x@ —R*, some kEN, @ ={y:{-r,-r +1 R*},*and*x, €@ is defined by x,(s ...##
###
Page 4099 of Mathematical Reviews Vol. , Issue 83j
[page]

1983
*
Mathematical Reviews
*

*Necessary*

*and*

*sufficient*

*conditions*

*for*asymptotic

*stability*

*of*the solution are obtained. ... 4099 34K Functional-differential

*and*differential-

*difference*

*equations*Integral sets are defined

*for*(1),

*and*

*sufficient*

*conditions*

*for*the existence

*of*the initial sets are determined

*and*their properties ...

##
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An Extension of the Kreiss Matrix Theorem

1988
*
SIAM Journal on Numerical Analysis
*

This new

doi:10.1137/0725071
fatcat:4bb6v2icyfetpizj7yhh4zqk5y
*condition*is important*for*the application*of*the theory*of*pseudo-*difference*operators to*stability*estimates*for*variable coefficient finite*difference**equations*. ... As an example*of*the usefulness*of*this new*condition*, we use it to prove*stability**of*the leap frog scheme*for*hyperbolic*equations*with variable coefficients. ... Theorem 121 gives*necessary**and**sufficient**conditions**for*the power*boundedness**of*a family*of*matrices. ...##
###
Page 3197 of Mathematical Reviews Vol. , Issue 89F
[page]

1989
*
Mathematical Reviews
*

*Necessary*

*and*

*sufficient*

*conditions*

*for*the asymptotic

*stability*

*of*the trivial solution

*and*

*sufficient*

*conditions*

*for*the oscillation

*of*all solutions

*of*first-

*order*neutral delay differential

*equations*...

*For*the

*equation*vx'(t) + x(t) = f(x(t-—1)), v > 0, the author gives

*conditions*on f

*for*the existence,

*for*all

*sufficient*small v, 34K Functional-differential

*and*differential-

*difference*

*equations*89f ...

##
###
Page 47 of Mathematical Reviews Vol. , Issue 90I
[page]

1990
*
Mathematical Reviews
*

Some

*sufficient*,*and*also*necessary**and**sufficient**conditions**for*asymptotic*stability**of*the trivial solution*of*some delay differential systems are obtained. ... The authors establish some algebraic*condition*,*necessary**and**sufficient**for*the zero solution*of*a linear system*of*autonomous*difference*-differential*equations**of*the type dx/dt = Ax(t)+ A,x(t — 7) + ...##
###
Asymptotic and boundedness behaviour of a second order difference equation

2020
*
Journal of computational mathematics
*

In this paper, we study the asymptotic behaviour

doi:10.26524/cm82
fatcat:oozpwuj7jbf3vlhjcutvqivpaq
*and**boundedness**of*the solutions*of*the*difference**equation*where λ > 1*and*α > 0, β > 0 are the immigration rate*and*population growth respectively*and*... initial*conditions*x −1 , x 0 are arbitrary positive numbers. ... (c) A*necessary**and**sufficient**condition**for*both roots*of*(6) to lie in the open unit disk |µ| < 1, is |p| < 1 − q < 2. ...##
###
Page 5608 of Mathematical Reviews Vol. , Issue 87j
[page]

1987
*
Mathematical Reviews
*

Gopalsamy (Adelaide)
Wen, Li Zhi (PRC-HUN) 87j:34145

*Boundedness**of*a class*of*second*order*differential*equations**and*second*order*differential-*difference**equations*. (Chinese. ... The region*of**stability*‘*for*all delays r’ is found*and*compared with that*for*the analogous differential-*difference**equation*.” R. F. ...##
###
A tribute to Ivan Kiguradze

2014
*
Boundary Value Problems
*

On oscillation

doi:10.1186/s13661-014-0228-x
fatcat:c6tdjjglcbh3rg5a74o2d46k5e
*conditions**for*solutions*of*the*equation*u + a(t)|u|*n*sign u = 0.Čas. Pěst. Mat. 87(4), 492-495 (1962) (in Russian) 3. ... On asymptotic properties*of*solutions*of*the*equation*u + a(t)|u|*n*sign u = 0. Soobshch. Akad. Nauk Gruz. SSR 30(2), 129-136 (1963) (in Russian) ... On the basis*of*these estimates, they obtained new*sufficient**conditions**for*the*boundedness*, uniform*stability*,*and*uniform asymptotic*stability**of*solutions*of*nonlinear delay differential systems [ ...##
###
Page 5581 of Mathematical Reviews Vol. , Issue 86m
[page]

1986
*
Mathematical Reviews
*

The author assumes that

*n*~1y(*n*) is bounded*and*gives*conditions**for*F which guarantee the*boundedness**of**n*~!z(*n*) or*of*Az(*n*). {*For*the entire collection see MR 86f:45002.} ... It also contains a result that gives a*sufficient**condition**for*finding an operator norm || - || such that, under this*condition*, the uniform asymp- totic*stability**for*all delays is equivalent to ||D( ...
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