A manifold of ground-state type solutions of semilinear elliptic equations
We consider the problem \[ -\Delta u(z,x) =g\bigl(u(z,x) \bigr),\;(z,x) \in(-l,l) \times \mathbb{R}^N, \quad u\in H^1\bigl((-l,l) \times\mathbb{R}^N \bigr) \] under periodic boundary conditions with respect to \(z\). The behaviour of ground state solutions to this problem is studied as \(l\to\infty\).
scientific article; zbMATH DE number 1037710