The third-order nonlinear difference equations a(p~A(~.A~.)) + q.f(~+p) = 0, p e {0,1, 2}, where (p,~), (rn), and (qn) are sequences of positive real numbers for n E N, f : R --\* ~ is a continuous function such that f(u)u > 0 for u =fi 0, are investigated. All nonoscillatory solutions of these equ
Global asymptotic stability of a family of difference equations
β Scribed by Xiaofan Yang; Yuan Yan Tang; Jianqiu Cao
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 236 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we study the difference equation
where ) are all continuous functions. We present a sufficient condition for this difference equation to have a globally asymptotically stable equilibrium c = 1. This condition generalizes some previous results.
π SIMILAR VOLUMES
In this work, we study the boundedness and the global asymptotic behavior of the solutions of the difference equation where Ξ± and Ξ² are positive real numbers, k β {1, 2, . . .} and the initial conditions y -k , . . . , y -1 , y 0 are arbitrary numbers.
In this paper, the rule for the lengths of positive and negative semicycles of nontrivial solutions of the following fourth-order rational difference equation, where a,b E [0, oo) and the initial values x-3,z-2, x-l,~c0 E (0, co), to successively occur is found to be...,4 +,3-, 1 +, 2-,2 +, 1-, 1 +