Multiple solutions of nonlinear elliptic Dirichlet problems in exterior domains
The authors consider the Dirichlet problem for the equation \(-\Delta u + \lambda^2u=u^{p-1}\) in an exterior domain \(\Omega\), with a subcritical \(p\). It is shown that there exist at least \(2k-1\) distinct positive solutions, provided the complement of \(\Omega\) consists of \(k\) sufficiently large connected components.
scientific article; zbMATH DE number 1389520