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Product Code:  MMONO/139 
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eBook ISBN:  9781470445478 
Product Code:  MMONO/139.E 
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Hardcover ISBN:  9780821846162 
eBook: ISBN:  9781470445478 
Product Code:  MMONO/139.B 
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Hardcover ISBN:  9780821846162 
Product Code:  MMONO/139 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445478 
Product Code:  MMONO/139.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821846162 
eBook ISBN:  9781470445478 
Product Code:  MMONO/139.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: 139; 1994; 348 ppMSC: Primary 35
The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad range of applications of topological methods to nonlinear differential equations is presented: solvability, estimation of the number of solutions, and the branching of solutions of nonlinear equations. Skrypnik establishes, by various procedures, a priori estimates and the regularity of solutions of nonlinear elliptic equations of arbitrary order. Also covered are methods of homogenization of nonlinear elliptic problems in perforated domains. The book is suitable for use in graduate courses in differential equations and nonlinear functional analysis.
ReadershipResearchers, mathematicians, and graduate students studying differential equations and nonlinear functional analysis.

Table of Contents

Chapters

Chapter 1. Mappings of monotone type and solvability of quasilinear boundary value problems

Chapter 2. Degree of generalized monotone mappings

Chapter 3. Topological characteristics of nonlinear elliptic boundary value problems

Chapter 4. Solvability and behavior of solutions of nonlinear elliptic boundary value problems

Chapter 5. Solvability of the nonlinear Dirichlet problem in a narrow strip

Chapter 6. Solvability of semilinear boundary value problems

Chapter 7. A priori estimates and regularity of solutions of higher order quasilinear elliptic equations

Chapter 8. Behavior of solutions of quasilinear elliptic equations near the boundary

Chapter 9. Nonlinear elliptic problems in domains with finegrained boundary

Chapter 10. Homogenization of nonlinear Dirichlet problems in domains with channels


Reviews

This is a nice and useful book representing a systematic approach to nonlinear elliptic partial differential equations with several interesting examples and applications.
Zentralblatt MATH


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The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad range of applications of topological methods to nonlinear differential equations is presented: solvability, estimation of the number of solutions, and the branching of solutions of nonlinear equations. Skrypnik establishes, by various procedures, a priori estimates and the regularity of solutions of nonlinear elliptic equations of arbitrary order. Also covered are methods of homogenization of nonlinear elliptic problems in perforated domains. The book is suitable for use in graduate courses in differential equations and nonlinear functional analysis.
Researchers, mathematicians, and graduate students studying differential equations and nonlinear functional analysis.

Chapters

Chapter 1. Mappings of monotone type and solvability of quasilinear boundary value problems

Chapter 2. Degree of generalized monotone mappings

Chapter 3. Topological characteristics of nonlinear elliptic boundary value problems

Chapter 4. Solvability and behavior of solutions of nonlinear elliptic boundary value problems

Chapter 5. Solvability of the nonlinear Dirichlet problem in a narrow strip

Chapter 6. Solvability of semilinear boundary value problems

Chapter 7. A priori estimates and regularity of solutions of higher order quasilinear elliptic equations

Chapter 8. Behavior of solutions of quasilinear elliptic equations near the boundary

Chapter 9. Nonlinear elliptic problems in domains with finegrained boundary

Chapter 10. Homogenization of nonlinear Dirichlet problems in domains with channels

This is a nice and useful book representing a systematic approach to nonlinear elliptic partial differential equations with several interesting examples and applications.
Zentralblatt MATH