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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| Format: | Article |
| Language: | English |
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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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| author | Stevo Stevic |
| author_facet | Stevo Stevic |
| author_sort | Stevo Stevic |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3162e02749854463b3da0f371fb9a1cd |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3162e02749854463b3da0f371fb9a1cd2025-08-20T02:38:53ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2007-01-01200710.1155/2007/5681356813Asymptotics of Some Classes of Higher-Order Difference EquationsStevo Stevic0Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000, SerbiaWe 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.http://dx.doi.org/10.1155/2007/56813 |
| spellingShingle | Stevo Stevic Asymptotics of Some Classes of Higher-Order Difference Equations Discrete Dynamics in Nature and Society |
| title | Asymptotics of Some Classes of Higher-Order Difference Equations |
| title_full | Asymptotics of Some Classes of Higher-Order Difference Equations |
| title_fullStr | Asymptotics of Some Classes of Higher-Order Difference Equations |
| title_full_unstemmed | Asymptotics of Some Classes of Higher-Order Difference Equations |
| title_short | Asymptotics of Some Classes of Higher-Order Difference Equations |
| title_sort | asymptotics of some classes of higher order difference equations |
| url | http://dx.doi.org/10.1155/2007/56813 |
| work_keys_str_mv | AT stevostevic asymptoticsofsomeclassesofhigherorderdifferenceequations |