Differential Equations with Involutions [Paperback]

This monograph covers the existing results regarding Greens functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators.The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Greens functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties.Obtaining a Greens function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.Involutions and differential equations.- General results for differential equations with involutions.- Order one problems with constant coefficients.- The non-constant case.- General linear equations.- A cone approximation to a problem with reflection.

First monograph on the subject

Many examples to illustrate the theory

Open problems to work on