Funciones de Green para Ecuaciones Diferenciales con Involuciones

TL;DR

This paper reviews recent advances in Green's functions for first-order differential equations with involutions, focusing on cases with initial conditions and boundary conditions, analyzing their properties and deriving new results.

Contribution

It introduces new Green's functions for differential equations with involutions under various conditions and studies their properties, including sign and related implications.

Findings

Derived Green's functions for specific involution problems

Analyzed the sign of Green's functions in these contexts

Established new theoretical results on differential equations with involutions

Abstract

In this work we revise the most recent developments concerning the study of first order problems regarding differential equations with involutions. We take into account two cases: the case of initial conditions and constant coefficients and the case of homogeneous boundary conditions and non-constant coefficients. Using different techniques, we obtain the Green's function for both problems, study its sign and derive further results.