Document Type
Report
Source Publication Title
Technical Report 8
Abstract
The study of Cauchy problem for differential equations in a Banach space has taken two different directions. One approach is to find compactness type conditions [1,2,4,9,14] to guarantee existence of solutions only and the corresponding results are extensions of the classical Peano's Theorem. The other approach is to employ accretive type conditions [9,10,11,12,15] which assure existence as well as uniqueness of solutions. In fact, this latter technic shows that uniqueness conditions imply existence of solutions [16]. In this paper we follow the first direction. Employing Lyapunov-like functions and the notion of the measure of noncompactness, we prove a local existence result which generalizes in a natural way the compactness type conditions. We also consider a global existence result under a general set of conditions so as to include existing results in this direction.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
3-1-1974
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Eisenfeld, Jerome and Lakshmikantham, V., "On the Existence of Solutions of Differential Equations in a Banach Space" (1974). Mathematics Technical Papers. 198.
https://mavmatrix.uta.edu/math_technicalpapers/198