Asymptotics of Some Classes of Higher-Order Difference Equations

Stevo Stevic

Discrete Dynamics in Nature and Society, 2007, vol. 2007, 1-20

Abstract:

We present some methods for finding asymptotics of some classes of nonlinear higher-order difference equations. Among others, we confirm a conjecture posed by S. Stević (2005). Monotonous solutions of the equation y n = A + ( y n − k / ∑ j = 1 m β j y n − q j ) p , n ∈ ℕ 0 , where p , A ∈ ( 0 , ∞ ) , k , m ∈ ℕ , q j , j ∈ { 1 , … , m } , are natural numbers such that q 1 < q 2 < ⋯ < q m , β j ∈ ( 0 , + ∞ ) , j ∈ { 1 , … , m } , ∑ j = 1 m β j = 1 , and y − s , y − s + 1 , … , y − 1 ∈ ( 0 , ∞ ) , where s = max { k , q m } , are found. A new inclusion theorem is proved. Also, some open problems and conjectures are posed.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:056813

DOI: 10.1155/2007/56813

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