![](/images/graphics-bg.png)
Interval Oscillation Criteria for Second-Order Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals
Author
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-17
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
By using a generalized arithmetic-geometric mean inequality on time scales, we study the forced oscillation of second-order dynamic equations with nonlinearities given by Riemann-Stieltjes integrals of the form [p(t)ϕα(xΔ(t))]Δ+q(t)ϕα(x(τ(t)))+∫aσ(b)r(t,s)ϕγ(s)(x(g(t,s)))Δξ(s)=e(t), where t∈[t0,∞)T=[t0,∞) ⋂ T, T is a time scale which is unbounded from above; ϕ*(u)=|u|*sgn u; γ:[a,b]T1→ℝ is a strictly increasing right-dense continuous function; p,q,e:[t0,∞)T→ℝ, r:[t0,∞)T×[a,b]T1→ℝ, τ:[t0,∞)T→[t0,∞)T, and g:[t0,∞)T×[a,b]T1→[t0,∞)T are right-dense continuous functions; ξ:[a,b]T1→ℝ is strictly increasing.
Some interval oscillation criteria are established in both the cases of delayed and advanced arguments.
As a special case, the work in this paper unifies and improves many existing results in the literature for equations with a finite number of nonlinear terms.
American Psychological Association (APA)
Sun, Yuangong. 2011. Interval Oscillation Criteria for Second-Order Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-14.
https://search.emarefa.net/detail/BIM-493188
Modern Language Association (MLA)
Sun, Yuangong. Interval Oscillation Criteria for Second-Order Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals. Abstract and Applied Analysis No. 2011 (2011), pp.1-14.
https://search.emarefa.net/detail/BIM-493188
American Medical Association (AMA)
Sun, Yuangong. Interval Oscillation Criteria for Second-Order Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-14.
https://search.emarefa.net/detail/BIM-493188
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-493188