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The Method of Upper, Lower Solutions and Volterra Integral Equations

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The Method of Upper, Lower Solutions and Volterra Integral Equations

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dc.contributor.author Ladde, G. S. en
dc.contributor.author Pachpatte, B. G. en
dc.contributor.author Lakshmikantham, V. en
dc.date.accessioned 2010-06-02T20:47:12Z en
dc.date.available 2010-06-02T20:47:12Z en
dc.date.issued 1980-12 en
dc.identifier.uri http://hdl.handle.net/10106/2254 en
dc.description.abstract In employing the method of upper and lower solutions to dynamical systems, one is required to impose a certain monotone property on the given system [5,6,11] When the given system does not possess such a monotonic property, stronger forms of upper and lower solutions have to be assumed in order to obtain similar results [4,6,9]. Furthermore, if the system enjoys a mixed monotone property the method of quasi-upper and lower solutions, which is recently introduced, is most useful [7]. In this paper we shall extend these ideas to Volterra integral equations. We want to note that Volterra integral equations and inequalities which can not be reduced to differential ones were first considered in [1,10], We shall first consider various aspects of Muller's type result and then develop monotone iterative technique to establish the existence of coupled quasi-minimal and maximal solutions. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;143 en
dc.subject Volterra integral equations en
dc.subject Mixed monotone property en
dc.subject Coupled solutions en
dc.subject.lcsh Volterra equations en
dc.subject.lcsh Mathematics Research en
dc.title The Method of Upper, Lower Solutions and Volterra Integral Equations en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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