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Existence and Comparison Results for Differential Equations of Sobolev Type

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Existence and Comparison Results for Differential Equations of Sobolev Type

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dc.contributor.author Vaughn, Randy en
dc.contributor.author Vatsala, A. S. en
dc.date.accessioned 2010-06-09T15:03:22Z en
dc.date.available 2010-06-09T15:03:22Z en
dc.date.issued 1978-12 en
dc.identifier.uri http://hdl.handle.net/10106/2424 en
dc.description.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.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;100 en
dc.subject Differential inequalities en
dc.subject Extremal solutions en
dc.subject Nonlinear Volterra integral equations en
dc.subject Peano type en
dc.subject Sobolev type en
dc.subject.lcsh Mathematics Research en
dc.title Existence and Comparison Results for Differential Equations of Sobolev Type en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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