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 i...

Full description

Bibliographic Details

Main Authors:	Cao, Daomin 1963- (Author), Peng, Shuangjie 1968- (Author), Yan, Shusen 1963- (Author)
Format:	Electronic eBook
Language:	English
Published:	Cambridge Cambridge University Press 2021
Series:	Cambridge studies in advanced mathematics
Subjects:	Differential equations, Elliptic Differential equations, Nonlinear Nichtlineare elliptische Differentialgleichung
Online Access:	BSB01 FHN01 Volltext
Summary:	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
Item Description:	Title from publisher's bibliographic system (viewed on 29 Jan 2021)
Physical Description:	1 Online-Ressource (ix, 252 Seiten)
ISBN:	9781108872638
DOI:	10.1017/9781108872638