Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale

Simple item page
dc.contributor.authorKaufmann, Eric R.
dc.contributor.authorRaffoul, Youssef N.
dc.date.accessioned2021-08-03T19:19:30Z
dc.date.available2021-08-03T19:19:30Z
dc.date.issued2007-02-12
dc.description.abstractLet T be a periodic time scale. We use a fixed point theorem due to Krasnosel'skiĭ to show that the nonlinear neutral dynamic equation with delay xΔ(t) = -α(t)xσ (t) + (Q(t, x(t), x(t - g(t)))))Δ + G(t, x(t), x(t - g(t))), t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the aid of the contraction mapping principle we study the asymptotic stability of the zero solution provided that Q(t, 0, 0) = G(t, 0, 0) = 0.
dc.description.departmentMathematics
dc.formatText
dc.format.extent12 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationKaufmann, E. R., & Raffoul, Y. N. (2007). Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale. <i>Electronic Journal of Differential Equations, 2007</i>(27), pp. 1-12.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14177
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectKrasnosel'skii
dc.subjectContraction mapping
dc.subjectNeutral
dc.subjectNonlinear
dc.subjectDelay
dc.subjectTime scales
dc.subjectPeriodic solution
dc.subjectUnique solution
dc.subjectStability
dc.titlePeriodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale
dc.typeArticle

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
kaufmann.pdf
Size:
250.26 KB
Format:
Adobe Portable Document Format
Description:
Download

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.54 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Electronic Journal of Differential Equations