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2 results

  • 3 - Local Uniqueness of Solutions

  • 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 129-155

  • Summary

    Chapter 3 is devoted to studying the local uniqueness of peak/bubbling solutions. In the 1990s, local uniqueness problems were discussed by the classical degree counting methods, which rely crucially on the estimates of the second order derivatives of the solutions. In this chapter, such problems are addressed by using the local Pohozaev identities.Such methods simplify the classical degree counting methods considerable.Once again, to avoid many sophisticated estimates,we choosenonlinear Schrodinger equations with subcritical growth and the Brezis-Nirenberg problem to illustrate the main techniques.