Higher-order energy expansions and spike locations (Q1890008)

The authors consider the following singularly perturbed semilinear elliptic problem: \[ \varepsilon^2\Delta u-bu+f(u)=0 \quad\text{in }\Omega, \qquad u>0\quad\text{in }\Omega \quad\text{and}\quad \frac{\partial u}{\partial\nu}=0 \quad\text{on }\partial\Omega, \tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb R^N\) with smooth boundary \(\partial\Omega\), \(\varepsilon>0\) is a small constant. They are interested in the higher-order energy expansions corresponding to (1) and spike locations.