Singularly Perturbed Methods for Nonlinear Elliptic Problems

Singularly Perturbed Methods for Nonlinear Elliptic Problems by Daomin Cao

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.

'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

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.

SKU	Nicht verfügbar
ISBN 13	9781108836838
ISBN 10	1108836836
Titel	Singularly Perturbed Methods for Nonlinear Elliptic Problems
Autor	Daomin Cao
Serie	Cambridge Studies In Advanced Mathematics
Buchzustand	Nicht verfügbar
Bindungsart	Hardback
Verlag	Cambridge University Press
Erscheinungsjahr	2021-02-18
Seitenanzahl	262
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
Hinweis	Nicht verfügbar