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arXiv · 1707.00857

Existence results for a linear equation with reflection, non-constant coefficient and periodic boundary conditions

Alberto Cabada·F. Adrián F. Tojo
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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.

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BibTeXRIS

Alberto Cabada, F. Adrián F. Tojo. 2017-07-04. Existence results for a linear equation with reflection, non-constant coefficient and periodic boundary conditions. https://arxiv.org/abs/1707.00857

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