Open Access Research

One-sided and two-sided Green’s functions

Rubens de Figueiredo Camargo1*, Ary Orozimbo Chiacchio2 and Edmundo Capelas de Oliveira2

Author affiliations

1 Departamento de Matemática, Faculdade de Ciências, Unesp, Bauru, SP, 17033-369, Brazil

2 Departamento de Matemática, Imecc, Unicamp, Campinas, SP, 13081-970, Brazil

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Citation and License

Boundary Value Problems 2013, 2013:45  doi:10.1186/1687-2770-2013-45

Published: 6 March 2013

Abstract

We discuss the one-sided Green’s function, associated with an initial value problem and the two-sided Green’s function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green’s functions and conclude which is the most convenient one. An incursion in the so-called fractional Green’s function is also presented. As an example, we discuss the isotropic harmonic oscillator.