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dc.contributor.authorVaughn, Randyen
dc.contributor.authorVatsala, A. S.en
dc.date.accessioned2010-06-09T15:03:22Zen
dc.date.available2010-06-09T15:03:22Zen
dc.date.issued1978-12en
dc.identifier.urihttp://hdl.handle.net/10106/2424en
dc.description.abstract**Please note that the full text is embargoed** ABSTRACT: Recently a new class of differential equations, called differential equations of Sobolev type was studied in [4] in which an existence theorem of Picards type was investigated as well as a variation of constants formula. In [5], existence and comparison results for a class of Volterra integral equation of Sobolev-type were discussed. In this paper we recall the Peano type existence result from [5] for Sobolev-differential equations and show that solutions can be extended to the entire square under consideration. This result extends results found in [1] for nonlinear Volterra integral equations. Our results include a comparison result in addition to the usual type of differential inequalities, and a differential inequality theorem such as Müller's [6]. This in turn proves the existence of extremal solutions. For special cases of the above results see [2,3,7]en
dc.language.isoen_USen
dc.publisherUniversity of Texas at Arlingtonen
dc.relation.ispartofseriesTechnical Report;100en
dc.subjectDifferential inequalitiesen
dc.subjectExtremal solutionsen
dc.subjectNonlinear Volterra integral equationsen
dc.subjectPeano typeen
dc.subjectSobolev typeen
dc.subject.lcshMathematics Researchen
dc.titleExistence and Comparison Results for Differential Equations of Sobolev Typeen
dc.typeTechnical Reporten
dc.publisher.departmentDepartment of Mathematicsen


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