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Published online by Cambridge University Press: 28 January 2021
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.
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