Solutions to nonlinear Schrödinger equations with singular electromagnetic potential and critical exponent

We investigate existence and qualitative behavior of solutions to nonlinear Schrödinger equations with critical exponent and singular electromagnetic potentials. We are concerned with magnetic vector potentials which are homogeneous of degree -1, including the Aharonov-Bohm class. In particular, by variational arguments we prove a result of multiplicity of solutions distinguished by symmetry properties. © 2011 Springer Basel AG