Singularly Perturbed Methods for Nonlinear Elliptic Problems
Hardcover 262 pages English March 25, 2021
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Cambridge University Press
Singularly Perturbed Methods for Nonlinear Elliptic Problems
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This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly investigating two relatively simple but typical non-compact elliptic problems. Each chapter then progresses to other related problems to help the reader learn more about the general theories developed from singularly perturbed methods. Designed for PhD students and junior mathematicians intending to do their research in the area of elliptic differential equations, the text covers three main topics. The first is the compactness of the minimization sequences, or the Palais-Smale sequences, or a sequence of approximate solutions; the second is the construction of peak or bubbling solutions by using the Lyapunov-Schmidt reduction method; and the third is the local uniqueness of these solutions.
- Author:
- Daomin Cao
- Publisher:
- Cambridge University Press
- Publication Date:
- March 25, 2021
- Number of pages:
- 262 pages
- Language:
- English
- Binding:
- Hardcover
- ISBN-10:
- 1108836836
- ISBN-13:
- 9781108836838