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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:412

Article

Cabada, Alberto¹  Tojo, F. Adrian F.¹ 

[1] Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat, Santiago De Compostela, Spain

关键词: Equations with involutions;    Equations with reflection;    Green's functions;    Maximum principles;    Comparison principles;    Periodic conditions;   

DOI  :  10.1016/j.jmaa.2013.10.067

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free