Document Type
Report
Source Publication Title
Technical Report 200
Abstract
We consider the first and second order periodic boundary value problems (PBVP for brevity)[see pdf for notation] and [see pdf for notation]and obtain the existence of extremal solutions as limits of monotone iterates. In [2] and [3], the monotone method was employed for the problems (1.1) and (1.2) when the corresponding lower and upper solutions a(t),B(t) satisfy [see pdf for notation] in addition to other conditions. Furthermore, when f is increasing, it is shown [2,3] that the conditions (1.3) and (1.4) are tantamount to assuming the existence of a periodic solution. Accordingly, the problem of proving the existence of periodic solutions when the conditions (1.3) and (1.4) are violated becomes important and this question has been open. Our main objective in this paper is to investigate this open problem.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
5-1-1982
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Lakshmikantham, V., "Remarks on First and Second Order Periodic Boundary Value Problems" (1982). Mathematics Technical Papers. 98.
https://mavmatrix.uta.edu/math_technicalpapers/98