Qualitative analysis of nonlinear elliptic partial differential equations

✍ Scribed by Vicentiu Radulescu

• Publisher: Hindawi Publishing Corporation
• Year: 2008
• Tongue: English
• Leaves: 205
• Series: Contemporary Mathematics and Its Applications Book Series
• Edition: First
• Category: Library

✦ Synopsis

The book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis.

Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence of nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions.

✦ Table of Contents

Front Cover......Page 1
Title Page......Page 2
Copyright Page......Page 5
Dedication......Page 6
Table of Contents......Page 8
Introduction......Page 10
1. Monotonicity methods for stationary equations......Page 14
2. Bifurcation problems......Page 44
3. Nonsmooth mountain pass theory......Page 68
4. Nonsmooth Ljusternik-Schnirelmann theory......Page 102
5. Multivalued elliptic problems......Page 128
Bibliography......Page 190
Index......Page 202