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Singularly Perturbed Methods for Nonlinear Elliptic Problems

£54.99

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: February 2021
  • availability: In stock
  • format: Hardback
  • isbn: 9781108836838

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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.

    • Provides self-contained materials for PhD students and junior mathematicians who wish to acquaint themselves with singularly perturbed methods
    • Makes the techniques understandable without involving too many sophisticated estimates
    • Discusses the general theories developed from the singularly perturbed methods
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    Reviews & endorsements

    'This book presents in a very nice and self-contained manner the main methods to find (or to construct) solutions, which exhibit a concentration property, to non-compact elliptic problems.' Lutz Recke, ZB Math Reviews

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    Product details

    • Date Published: February 2021
    • format: Hardback
    • isbn: 9781108836838
    • length: 262 pages
    • dimensions: 234 x 151 x 19 mm
    • weight: 0.49kg
    • availability: In stock
  • Table of Contents

    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.

  • Authors

    Daomin Cao, Chinese Academy of Sciences, Beijing
    Daomin Cao is a professor at the Institute of Applied Mathematics, Chinese Academy of Sciences. His research focuses on nonlinear partial differential equations. He was awarded the first-class prize of Outstanding Young Scientists of Chinese Academy of Sciences. He is the editor of academic mathematical journals including Applicable Analysis, Annales Academiac Scientiarum Fennicae Mathematica, and Acta Mathematicae Applicatae Sinica.

    Shuangjie Peng, Central China Normal University
    Shuangjie Peng is a professor at the School of Mathematics and Statistics, Central China Normal University. His research focuses on nonlinear elliptic problems. He was awarded the first-class prize of Natural Sciences of Hubei province and the second-class prize of Natural Sciences from the Ministry of Education. He is the editor of academic mathematical journals including Communications on Pure and Applied Analysis, Acta Mathematica Scientia, and Acta Mathematicae Applicatae Sinica.

    Shusen Yan, Central China Normal University
    Shusen Yan is a professor at the School of Mathematics and Statistics, Central China Normal University. His main research interests are in nonlinear elliptic problems.

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