Asymptotic solutions of forced nonlinear second order differential equations and their extensions

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dc.contributor.authorMingarelli, Angelo B.
dc.contributor.authorSadarangani, Kishin
dc.date.accessioned2021-08-05T14:01:42Z
dc.date.available2021-08-05T14:01:42Z
dc.date.issued2007-03-09
dc.description.abstractUsing a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented.
dc.description.departmentMathematics
dc.formatText
dc.format.extent40 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationMingarelli, A. B., & Sadarangani, K. (2007). Asymptotic solutions of forced nonlinear second order differential equations and their extensions. <i>Electronic Journal of Differential Equations, 2007</i>(40), pp. 1-40.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14200
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, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectSecond order differential equations
dc.subjectNonlinear
dc.subjectNon-oscillation
dc.subjectIntegral inequalities
dc.subjectAtkinson's theorem
dc.subjectAsymptotically linear
dc.subjectAsymptotically constant
dc.subjectOscillation
dc.subjectDifferential inequalities
dc.subjectFixed point theorem
dc.subjectVolterra-Stieltjes
dc.subjectIntegral equations
dc.titleAsymptotic solutions of forced nonlinear second order differential equations and their extensions
dc.typeArticle

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