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 | **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.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 |