On the Schrödinger equation involving a critical Sobolev exponent and magnetic field (Q2386869)

This paper is devoted to the study of entire solutions of the semilinear Schrödinger equation \(-\Delta_Au+V(x)u=Q(x)| u| ^{2^*-2}u\), where \(V\) is a sign-changing potential. The main result of the paper establishes the existence of nontrivial solutions \(u\) in the weighted Sobolev space \(H^1_{A,V^+}(\mathbb R^N)\). The proof relies on min-max arguments based on a topological linking.