A pointwise finite dimensional reduction method

The investigation of stability and instability properties for nonlinear elliptic PDEs has been the target of intense investigation in the last decades, the most celebrated results being probably the compactness and noncompactness results for the set of solutions of the Yamabe equation. Instability results are usually obtained through a constructive method, called a finite-dimensional reduction method. In this talk, to investigate non-compactness issues for a highly coupled system of elliptic PDEs where the usual methods are ineffective, I will describe a new finite-dimensional reduction method which merges the traditional energy approach with asymptotic analysis techniques.