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dc.contributor.authorAppleby, John ( )
dc.contributor.authorPatterson, Denis ( Orcid Icon 0000-0002-4509-7294 )
dc.date.accessioned2022-03-21T14:23:07Z
dc.date.available2022-03-21T14:23:07Z
dc.date.issued2017-01-16
dc.identifier.citationAppleby, J. A., D., & Patterson, D. D. (2017). Hartman-Wintner growth results for sublinear functional differential equations. Electronic Journal of Differential Equations, 2017(21), pp. 1-45.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15526
dc.description.abstractThis article determines the rate of growth to infinity of scalar autonomous nonlinear functional and Volterra differential equations. In these equations, the right-hand side is a positive continuous linear functional of ƒ(x). We assume ƒ grows sublinearly, leading to subexponential growth in the solutions. The main results show that the solution of the functional differential equations are asymptotic to that of an auxiliary autonomous ordinary differential equation with right-hand side proportional to ƒ. This happens provided ƒ grows more slowly than l(x) = x/log x. The linear-logarithmic growth rate is also shown to be critical: if ƒ grows more rapidly than l, the ODE dominates the FDE; if ƒ is asymptotic to a constant multiple of l, the FDE and ODE grow at the same rate, modulo a constant non-unit factor; if ƒ grows more slowly than l, the ODE and FDE grow at exactly the same rate. A partial converse of the last result is also proven. In the case when the growth rate is slower than that of the ODE, sharp bounds on the growth rate are determined. The Volterra and finite memory equations can have differing asymptotic behaviour and we explore the source of these differences.
dc.formatText
dc.format.extent45 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectFunctional differential equationsen_US
dc.subjectVolterra equationsen_US
dc.subjectAsymptoticsen_US
dc.subjectSubexponential growthen_US
dc.subjectBounded delayen_US
dc.subjectUnbounded delayen_US
dc.titleHartman-Wintner growth results for sublinear functional differential equationsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.holderCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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