Differential Equations with Involutions / by Alberto Cabada, F. Adrián F. Tojo.

Format:

Book

Author/Creator:

Cabada, Alberto, Author.

F. Tojo, F. Adrián., Author.

Series:

Atlantis Briefs in Differential Equations, 2405-6413

Language:

English

Subjects (All):

Differential equations.

Mathematical physics.

Differential Equations.

Mathematical Methods in Physics.

Local Subjects:

Differential Equations.

Mathematical Methods in Physics.

Physical Description:

1 online resource (160 p.)

Edition:

1st ed. 2015.

Place of Publication:

Paris : Atlantis Press : Imprint: Atlantis Press, 2015.

Language Note:

English

Summary:

This monograph covers the existing results regarding Green’s 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 Green’s 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 Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.

Contents:

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.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

94-6239-121-1