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2 - Perturbation Methods

Published online by Cambridge University Press:  28 January 2021

Daomin Cao ,
Shuangjie Peng  and
Shusen Yan
Daomin Cao
Affiliation:
Chinese Academy of Sciences, Beijing
Shuangjie Peng
Affiliation:
Central China Normal University
Shusen Yan
Affiliation:
Central China Normal University
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Summary

The Lyapunov-Schmidt reduction method and its variants have been widely used to construct peak solutions or bubbling solutions for singularly perturbed elliptic problems. In Chapter 2, we discuss the existence of such solutions, as well as the necessary condition for the location of the concentration points of the solutions.As illustrations of the main idea, we study two typical singularly perturbed elliptic problems in Chapter 2, and they are the nonlinear Schrodinger equations with subcritical growth and the Brezis-Nirenberg problem. Problems have been chosen so that many sophisticated estimates can be avoided.

Keywords

Lyapunov-Schmidt reductionPohozaev identitiespeak solutionsbubbling solutions
Type
Chapter
Information
Singularly Perturbed Methods for Nonlinear Elliptic Problems , pp. 54 - 128
Publisher: Cambridge University Press
Print publication year: 2021

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