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Singularly Perturbed Methods for Nonlinear Elliptic Problems

Singularly Perturbed Methods for Nonlinear Elliptic Problems

Singularly Perturbed Methods for Nonlinear Elliptic Problems

Daomin Cao, Chinese Academy of Sciences, Beijing
Shuangjie Peng, Central China Normal University
Shusen Yan, Central China Normal University
February 2021
Available
Hardback
9781108836838
£60.99
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Hardback
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eBook

    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

    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

    See more reviews

    Product details

    February 2021
    Hardback
    9781108836838
    262 pages
    234 × 151 × 19 mm
    0.49kg
    Available

    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.