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The Existence of Periodic and Subharmonic Solutions of Subquadratic Second Order Difference Equations
Author(s) -
Guo Zhiming,
Yu Jianshe
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004563
Subject(s) - subharmonic , order (exchange) , critical point (mathematics) , integer (computer science) , mathematics , mathematical analysis , mathematical physics , physics , nonlinear system , quantum mechanics , finance , economics , computer science , programming language
By critical point theory, a new approach is provided to study the existence of periodic and subharmonic solutions of the second order difference equationΔ 2 x n ‐ 1 + f ( n , x n ) = 0 ,where f ∈ C (R × R m , R m ), f ( t + M , z )+ f ( t , z ) for any ( t, z )∈R × R m and M is a positive integer. This is probably the first time critical point theory has been applied to deal with the existence of periodic solutions of difference systems.