RESEARCH COMMONS
LIBRARY

Existence and Comparison Results for Differential Equations of Sobolev Type

ResearchCommons/Manakin Repository

Existence and Comparison Results for Differential Equations of Sobolev Type

Show full item record

Title: Existence and Comparison Results for Differential Equations of Sobolev Type
Author: Vaughn, Randy; Vatsala, A. S.
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]
URI: http://hdl.handle.net/10106/2424
Date: 1978-12

Files in this item

Files Size Format View Description
MathTechReport0100.pdf 416.3Kb PDF View/Open PDF

This item appears in the following Collection(s)

Show full item record

Browse

My Account

Statistics

About Us