Existence results for a linear equation with reflection, non-constant coefficient and periodic boundary conditions
Classical Analysis and ODEs
2017-07-05 v1
Abstract
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our attention to the case of the reflection. We study then different cases for which a Green's function can be obtained explicitly and derive several results in order to obtain information about its sign. Once the sign is known, maximum and anti-maximum principles follow. We end this work with more general existence and uniqueness of solution results.
Keywords
Cite
@article{arxiv.1707.00857,
title = {Existence results for a linear equation with reflection, non-constant coefficient and periodic boundary conditions},
author = {Alberto Cabada and F. Adrián F. Tojo},
journal= {arXiv preprint arXiv:1707.00857},
year = {2017}
}