Existence and multiplicity of positive solutions of semilinear elliptic equations in unbounded domains
The paper deals with semilinear elliptic equations of the following form \[ -\Delta u+u= Q(x) |u|^{p-2}u \] in an exterior domain of \(\mathbb R^N\). The authors give some existence and multiplicity results for positive solutions when the potential \(Q(x)\) is bounded, tends to a positive constant at infinity and may change sign. The methods are based on the investigation of the interaction of \(Q\) and on the properties of the topology of exterior domains very close to \(\mathbb R^N\).
scientific article; zbMATH DE number 5918266