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5 - A Compactness Theorem and Application

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

Chapter 5 is devoted to studying the non-existence of concentration solutions for other singularly perturbed elliptic problems. Results in this direction are obtained by using a local Pohozaev identity. As an application of these results, the existence of infinitely many sign-changing solutions for the Brezis-Nirenberg problem is proved.

Keywords

Global compactnesssign-changing solutionsmultiplicity
Type
Chapter
Information
Singularly Perturbed Methods for Nonlinear Elliptic Problems , pp. 179 - 204
Publisher: Cambridge University Press
Print publication year: 2021

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