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1 - Non-compact Elliptic Problems

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

This chapter is devoted to studying the existence of the least energy solutions for Schrodinger equations with subcritical growth and semilinear elliptic problems involving a Sobolev critical exponent in bounded domains. One of the main topics is to discuss how the compactness of the minimization sequences, or the Palais-Smale sequences, can be recovered by an energy constraint. Gloobal compactness results, which shows how a Palais-Smale sequence may lose its compactness, are also discussed. This chapter serves as a preliminary for the topics discussed in the subsequent chapters of this book.

Keywords

Mountain passconcentration compactnessglobal compactnessleast energy solutions
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Chapter
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Singularly Perturbed Methods for Nonlinear Elliptic Problems , pp. 1 - 53
Publisher: Cambridge University Press
Print publication year: 2021

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