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Published online by Cambridge University Press: 28 January 2021
The Lyapunov-Schmidt reduction method and its variants have been widely used to construct peak solutions or bubbling solutions for singularly perturbed elliptic problems. In Chapter 2, we discuss the existence of such solutions, as well as the necessary condition for the location of the concentration points of the solutions.As illustrations of the main idea, we study two typical singularly perturbed elliptic problems in Chapter 2, and they are the nonlinear Schrodinger equations with subcritical growth and the Brezis-Nirenberg problem. Problems have been chosen so that many sophisticated estimates can be avoided.
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