Document Type
Report
Source Publication Title
Technical Report 100
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]
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
12-1-1978
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Vaughn, Randy and Vatsala, A. S., "Existence and Comparison Results for Differential Equations of Sobolev Type" (1978). Mathematics Technical Papers. 145.
https://mavmatrix.uta.edu/math_technicalpapers/145