Periodicity and stability in neutral nonlinear differential equations with functional delay

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dc.contributor.authorDib, Youssef M.
dc.contributor.authorMaroun, Mariette R.
dc.contributor.authorRaffoul, Youssef N.
dc.date.accessioned2021-07-13T20:23:33Z
dc.date.available2021-07-13T20:23:33Z
dc.date.issued2005-12-06
dc.description.abstractWe 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.description.departmentMathematics
dc.formatText
dc.format.extent11 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationDib, Y. M., Maroun, M. R., & Raffoul, Y. N. (2005). Periodicity and stability in neutral nonlinear differential equations with functional delay. <i>Electronic Journal of Differential Equations, 2005</i>(142), pp. 1-11.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13867
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectKrasnoselskii
dc.subjectContraction
dc.subjectNeutral differential equation
dc.subjectIntegral equation
dc.subjectPeriodic solution
dc.subjectAsymptotic stability
dc.titlePeriodicity and stability in neutral nonlinear differential equations with functional delay
dc.typeArticle

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