3 - Local Uniqueness of Solutions

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.