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Oscillation Criteria for Second-Order Delay, Difference, and Functional Equations
Joint Authors
Stavroulakis, I. P.
Kikina, Luljeta
Source
International Journal of Differential Equations
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-04-01
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
Consider the second-order linear delay differential equation x′′(t)+p(t)x(τ(t))=0, t≥t0, where p∈C([t0,∞),ℝ+), τ∈C([t0,∞),ℝ), τ(t) is nondecreasing, τ(t)≤t for t≥t0 and limt→∞τ(t)=∞, the (discrete analogue) second-order difference equation Δ2x(n)+p(n)x(τ(n))=0, where Δx(n)=x(n+1)−x(n), Δ2=Δ∘Δ, p:ℕ→ℝ+, τ:ℕ→ℕ, τ(n)≤n−1, and limn→∞τ(n)=+∞, and the second-order functional equation x(g(t))=P(t)x(t)+Q(t)x(g2(t)), t≥t0, where the functions P, Q∈C([t0,∞),ℝ+), g∈C([t0,∞),ℝ), g(t)≢t for t≥t0, limt→∞g(t)=∞, and g2 denotes the 2th iterate of the function g, that is, g0(t)=t, g2(t)=g(g(t)), t≥t0.
The most interesting oscillation criteria for the second-order linear delay differential equation, the second-order difference equation and the second-order functional equation, especially in the case where liminft→∞∫τ(t)tτ(s)p(s)ds≤1/e and limsupt→∞∫τ(t)tτ(s)p(s)ds<1 for the second-order linear delay differential equation, and 0
American Psychological Association (APA)
Kikina, Luljeta& Stavroulakis, I. P.. 2010. Oscillation Criteria for Second-Order Delay, Difference, and Functional Equations. International Journal of Differential Equations،Vol. 2010, no. 2010, pp.1-14.
https://search.emarefa.net/detail/BIM-483966
Modern Language Association (MLA)
Kikina, Luljeta& Stavroulakis, I. P.. Oscillation Criteria for Second-Order Delay, Difference, and Functional Equations. International Journal of Differential Equations No. 2010 (2010), pp.1-14.
https://search.emarefa.net/detail/BIM-483966
American Medical Association (AMA)
Kikina, Luljeta& Stavroulakis, I. P.. Oscillation Criteria for Second-Order Delay, Difference, and Functional Equations. International Journal of Differential Equations. 2010. Vol. 2010, no. 2010, pp.1-14.
https://search.emarefa.net/detail/BIM-483966
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-483966