Singularly perturbed methods for nonlinear elliptic problems
著者
書誌事項
Singularly perturbed methods for nonlinear elliptic problems
（Cambridge studies in advanced mathematics, 191）
Cambridge University Press, 2021
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注記
Includes bibliographical references (p. 242-250) and index
内容説明・目次
内容説明
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.
目次
- 1. Non-Compact Elliptic Problems
- 2. Perturbation Methods
- 3. Local Uniqueness of Solutions
- 4. Construction of Infinitely Many Solutions
- 5. A Compactness Theorem and Application
- 6. The Appendix.
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