Document Type
Report
Source Publication Title
Technical Report 46
Abstract
Monotone iterative methods have been successfully used to generate improvable two-sided point-wise bounds on solutions of nonlinear boundary value problems for both ordinary and partial differential equations. While such procedures take a simple form when the nonlinearities are independent of gradient terms [6,9], the extension of such techniques to fully nonlinear problems has been quite formidable. In the case of scalar ordinary differential equations of the type (1.1) [see PDF for equation] such results have been obtained making use of either a linear maximum principle (3,1] or a nonlinear maximum principle [4]. In either case an essential use is made of a Nagumo-type condition [5] for deriving uniform estimates on the gradient. The lack of similar tools for higher dimensional problems has impeded comparable progress in obtaining similar results for equations of the type.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
8-1-1976
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Lakshmikantham, V.; Chandra, Jagdish; and Leela, S., "A Monotone Method for Infinite System of Nonlinear Boundary Value Problems" (1976). Mathematics Technical Papers. 216.
https://mavmatrix.uta.edu/math_technicalpapers/216