Document Type
Report
Source Publication Title
Technical Report 11
Abstract
The study of the Cauchy problem for differential equations in a Banach space has taken two different directions. One direction is to find compactness type conditions that guarantee only existence of solutions and the corresponding results are extensions of the classical Peano's theorem. The other approach is to employ monotonicity (accretive or dissipative) type conditions that assure existence as well as uniqueness of solutions. In fact, this latter method shows that uniqueness conditions imply existence of solutions also [37] and therefore may be regarded as extensions of the classical Picard's theorem.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
7-1-1974
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Lakshmikantham, V., "Existence and Comparison Results for Differential Equations in a Banach Space" (1974). Mathematics Technical Papers. 120.
https://mavmatrix.uta.edu/math_technicalpapers/120