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2 results

  • 1 - Non-compact Elliptic Problems

  • Daomin Cao, Chinese Academy of Sciences, Beijing, Shuangjie Peng, Shusen Yan
  • Book:
    Singularly Perturbed Methods for Nonlinear Elliptic Problems
    Published online:
    28 January 2021
    Print publication:
    18 February 2021, pp 1-53

  • 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.