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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

Sk. Sarif Hassan, Esha Chatterjee, Thanh Tran
2015 Cogent Mathematics  
We investigate the dynamics 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.  ... 
doi:10.1080/23311835.2015.1122276 fatcat:r4ueadp3xbbkvg76czbsfmiism

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  ... 

An Extension of the Kreiss Matrix Theorem

John C. Strikwerda, Bruce A. Wade
1988 SIAM Journal on Numerical Analysis  
This new 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.  ... 
doi:10.1137/0725071 fatcat:4bb6v2icyfetpizj7yhh4zqk5y

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

Dilip D S, Smitha Mary Mathew, Elsayed E M
2020 Journal of computational mathematics  
In this paper, we study the asymptotic behaviour 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.  ... 
doi:10.26524/cm82 fatcat:oozpwuj7jbf3vlhjcutvqivpaq

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 stabilityfor all delays r’ is found and compared with that for the analogous differential-difference equation.” R. F.  ... 

A tribute to Ivan Kiguradze

Irena Rachůnková, Svatoslav Staněk, Milan Tvrdý, Aleksandre Lomtatidze, Ravi P Agarwal, Irina Astashova, Alexander Domoshnitsky, Zuzana Došlá, Vyacheslav M Evtukhov, Nicolai A Izobov, Takasi Kusano, Nino Partsvania (+4 others)
2014 Boundary Value Problems  
On oscillation 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 [  ... 
doi:10.1186/s13661-014-0228-x fatcat:c6tdjjglcbh3rg5a74o2d46k5e

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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