Solutions of the first order linear equation with reflection and general linear conditions

2017/07/04 by Alberto Cabada, Cabada, Alberto, Tojo, F. Adrián F. +1
Computer Science · Engineering · Mathematics · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Material Science and Thermodynamics #Matrix Theory and Algorithms #Numerical methods for differential equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1707.00841

openalex publication_date 2017/07/04 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

This work is devoted to the study of first order linear problems with involution and general linear conditions. We first study the problem in the case of antiperiodic boundary conditions, giving an explicit Green's function for it. Then we move forward to more general linear boundary conditions, focusing on sufficient conditions for existence and uniqueness of solution. At the end of the paper we give estimates that ensure the positivity of the solution in the general problems and illustrate these applications with examples.

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