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  3. Singularly Perturbed Methods for Nonlinear Elliptic Problems
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2021
      February 2021
      ISBN:
      9781108872638
      9781108836838
      DOI:
      https://doi.org/10.1017/9781108872638
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.49kg, 262 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
      Series:
      Cambridge Studies in Advanced Mathematics
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    Subjects:
    Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
    Series:
    Cambridge Studies in Advanced Mathematics
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    Book description

    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.

    Reviews

    ‘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 Source: ZB Math Reviews

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