
Hardcover ISBN: | 978-0-8218-0586-2 |
Product Code: | MMONO/160 |
List Price: | $165.00 |
MAA Member Price: | $148.50 |
AMS Member Price: | $132.00 |
eBook ISBN: | 978-1-4704-4575-1 |
Product Code: | MMONO/160.E |
List Price: | $155.00 |
MAA Member Price: | $139.50 |
AMS Member Price: | $124.00 |
Hardcover ISBN: | 978-0-8218-0586-2 |
eBook: ISBN: | 978-1-4704-4575-1 |
Product Code: | MMONO/160.B |
List Price: | $320.00 $242.50 |
MAA Member Price: | $288.00 $218.25 |
AMS Member Price: | $256.00 $194.00 |

Hardcover ISBN: | 978-0-8218-0586-2 |
Product Code: | MMONO/160 |
List Price: | $165.00 |
MAA Member Price: | $148.50 |
AMS Member Price: | $132.00 |
eBook ISBN: | 978-1-4704-4575-1 |
Product Code: | MMONO/160.E |
List Price: | $155.00 |
MAA Member Price: | $139.50 |
AMS Member Price: | $124.00 |
Hardcover ISBN: | 978-0-8218-0586-2 |
eBook ISBN: | 978-1-4704-4575-1 |
Product Code: | MMONO/160.B |
List Price: | $320.00 $242.50 |
MAA Member Price: | $288.00 $218.25 |
AMS Member Price: | $256.00 $194.00 |
-
Book DetailsTranslations of Mathematical MonographsVolume: 160; 1997; 104 ppMSC: Primary 35
The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation \(F(\dot y,y,x)=0\). Taking as linearization the first order operator \(Lu=C_{ij}u_{x_j}^i+C_iu^i\), one can, under certain conditions, regard the operator \(L\) as a compact perturbation of the operator div.
This book presents results on boundary-value problems for \(L\) and the theory of nonlinear perturbations of \(L\). Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator \(L\). An analog of the Weyl decomposition is proved.
The book also contains a local description of the set of all solutions (located in a small neighborhood of a known solution) to the boundary-value problems for the nonlinear equation \(F(\dot y, y, x) = 0\) for which \(L\) is a linearization. A classification of sets of all solutions to various boundary-value problems for the nonlinear equation \(F(\dot y, y, x) = 0\) is given.
The results are illustrated by various applications in geometry, the calculus of variations, physics, and continuum mechanics.
ReadershipGraduate students and research mathematicians interested in partial differential equations.
-
Table of Contents
-
Chapters
-
Chapter 1. Linear perturbations of the operator div
-
Chapter 2. Nonlinear perturbations of the operator div
-
Appendix
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation \(F(\dot y,y,x)=0\). Taking as linearization the first order operator \(Lu=C_{ij}u_{x_j}^i+C_iu^i\), one can, under certain conditions, regard the operator \(L\) as a compact perturbation of the operator div.
This book presents results on boundary-value problems for \(L\) and the theory of nonlinear perturbations of \(L\). Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator \(L\). An analog of the Weyl decomposition is proved.
The book also contains a local description of the set of all solutions (located in a small neighborhood of a known solution) to the boundary-value problems for the nonlinear equation \(F(\dot y, y, x) = 0\) for which \(L\) is a linearization. A classification of sets of all solutions to various boundary-value problems for the nonlinear equation \(F(\dot y, y, x) = 0\) is given.
The results are illustrated by various applications in geometry, the calculus of variations, physics, and continuum mechanics.
Graduate students and research mathematicians interested in partial differential equations.
-
Chapters
-
Chapter 1. Linear perturbations of the operator div
-
Chapter 2. Nonlinear perturbations of the operator div
-
Appendix