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dc.contributor.authorDib, Youssef M. ( Orcid Icon 0000-0003-3388-4749 )
dc.contributor.authorMaroun, Mariette R. ( )
dc.contributor.authorRaffoul, Youssef N. ( )
dc.identifier.citationDib, Y. M., Maroun, M. R., & Raffoul, Y. N. (2005). Periodicity and stability in neutral nonlinear differential equations with functional delay. Electronic Journal of Differential Equations, 2005(142), pp. 1-11.en_US

We study the existence and uniqueness of periodic solutions and the stability of the zero solution of the nonlinear neutral differential equation

d/dt x(t) = -α(t)x(t) + d/dt Q(t, x(t - g(t))) + G(t, x(t), x(t - g(t))).

In the process we use integrating factors and convert the given neutral differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this neutral differential equation. We also use the contraction mapping principle to show the existence of a unique periodic solution and the asymptotic stability of the zero solution provided that Q(0, 0) = G(t, 0, 0) = 0.

dc.format.extent11 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectNeutral differential equationen_US
dc.subjectIntegral equationen_US
dc.subjectPeriodic solutionen_US
dc.subjectAsymptotic stabilityen_US
dc.titlePeriodicity and stability in neutral nonlinear differential equations with functional delayen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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