Singular variation of the ground state eigenvalue for a semilinear elliptic equation (Q1313225)

The author studies the problem \(-\Delta u= \lambda u^ p\) in \(M_ \varepsilon\), \(u=0\) on \(\partial M_ \varepsilon\), \(u>0\) in \(M_ \varepsilon\). Here \(M_ \varepsilon\) is a bounded domain in \(\mathbb{R}^ 3\) with a ball of radius \(\varepsilon\) removed from the interior and \(1<p<5\). He considers the solution \(u_ \varepsilon\) which minimizes the natural constrained variational principle and the corresponding \(\lambda(\varepsilon)\). In particular, he studies how \(\lambda(\varepsilon)\) varies with \(\varepsilon\).