Singularly Perturbed Methods for Nonlinear Elliptic Problems

Daomin Cao (Chinese Academy of Sciences, Beijing), Shuangjie Peng, Shusen Yan

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English

Cambridge University Press
18 February 2021

Differential calculus & equations; Numerical analysis

Series: Cambridge Studies in Advanced Mathematics

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.

By: Daomin Cao (Chinese Academy of Sciences Beijing), Shuangjie Peng, Shusen Yan
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 151mm, Spine: 19mm
Weight: 490g
ISBN: 9781108836838
ISBN 10: 1108836836
Series: Cambridge Studies in Advanced Mathematics
Pages: 262
Publication Date: 18 February 2021
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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

Reviews for Singularly Perturbed Methods for Nonlinear Elliptic Problems

'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