Asymptotics of Some Classes of Higher-Order Difference Equations
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 yn=A+(yn−k/∑j=1mβjyn−qj)p, n∈ℕ0, where p,A∈(0,∞), k,m∈ℕ, qj,j∈{1,…,m}, are natural num...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2007/56813 |
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| Summary: | 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
yn=A+(yn−k/∑j=1mβjyn−qj)p, n∈ℕ0, where p,A∈(0,∞), k,m∈ℕ, qj,j∈{1,…,m}, are natural numbers such that q1<q2<⋯<qm,βj∈(0,+∞), j∈{1,…,m}, ∑j=1mβj=1, and y−s,y−s+1,…,y−1∈(0,∞), where s=max{k,qm}, are found. A new inclusion theorem is proved. Also, some open problems and conjectures are posed. |
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| ISSN: | 1026-0226 1607-887X |