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Oscillation and Nonoscillation of a Class of Functional Equations
Author(s) -
Zhang B.G.,
Choi S.K.
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200107)227:1<159::aid-mana159>3.0.co;2-d
Subject(s) - oscillation (cell signaling) , mathematics , integer (computer science) , class (philosophy) , set (abstract data type) , mathematical analysis , pure mathematics , combinatorics , chemistry , computer science , artificial intelligence , biochemistry , programming language
In this paper, we consider the following equation$$x(g(t)) = p(t)x(t)+\sum ^m_{i=1} Q_i (t)x(g^{k+i} (t)) \, ,$$where p , Q i : I → ℝ + = (0, ∞), i = 1, 2, ..., m , I ⊂ (0, ∞) is an unbounded set, g : I → I , g ( t ) ≢ t , lim t →∞ g ( t ) = ∞, t ∈ I , k ≥ 1 is a positive integer. Some oscillation and nonoscillation criteria are obtained.