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4 - Construction of Infinitely Many Solutions

Published online by Cambridge University Press:  28 January 2021

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 are usually used to construct solutions for elliptic problems without small parameters. In Chapter 4, these methods are adapted to study the Schrodinger equations with subcritical growth. The results in Chapter 4 show that the non-compactness of some elliptic problems may give rise to the existence of infinitely many positive solutions whose energy can be arbitrarily large. Such results cannot be obtained by using the abstract critical points theories.

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Publisher: Cambridge University Press
Print publication year: 2021

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