This introduction to the singularly perturbed methods in the
nonlinear elliptic partial differential equations emphasises the
existence and local uniqueness of solutions exhibiting
concentration property. The authors avoid using sophisticated
estimates and explain the main techniques by thoroughly
investigating two relatively simple but typical non-compact
elliptic problems. Each chapter then progresses to other related
problems to help the reader learn more about the general theories
developed from singularly perturbed methods. Designed for PhD
students and junior mathematicians intending to do their research
in the area of elliptic differential equations, the text covers
three main topics. The first is the compactness of the minimization
sequences, or the Palais-Smale sequences, or a sequence of
approximate solutions; the second is the construction of peak or
bubbling solutions by using the Lyapunov-Schmidt reduction method;
and the third is the local uniqueness of these solutions.
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