Solutions and Green's function of the first order linear equation with reflection and initial conditions

被引：15

作者：

Cabada, Alberto ^{[1
]}

Fernandez Tojo, Fernando Adrian ^{[1
]}

机构：

[1] Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat, Santiago De Compostela 15706, Galicia, Spain

来源：

BOUNDARY VALUE PROBLEMS | 2014年

关键词：

equations with involutions; equations with reflection; Green's functions; maximum principles; comparison principles; periodic conditions; ALMOST-PERIODIC SOLUTIONS; DIFFERENTIAL-EQUATIONS; ARGUMENT; INEQUALITIES; EXISTENCE; THEOREMS; QUESTION;

D O I：

10.1186/1687-2770-2014-99

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work is devoted to the study of the existence and sign of Green's functions for first order linear problems with constant coefficients and initial (one point) conditions. We first prove a result on the existence of solutions of nth order linear equations with involutions via some auxiliary functions to later prove a uniqueness result in the first order case. We study then different situations for which a Green's function can be obtained explicitly and derive several results in order to obtain information as regards the sign of the Green's function. Once the sign is known, optimal maximum and anti-maximum principles follow.

引用

页数：16

共 25 条

[1] BOUNDED SOLUTIONS FOR DIFFERENTIAL-EQUATIONS WITH REFLECTION OF THE ARGUMENT [J].