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We investigate existence and qualitative behaviour of solutions to nonlinearSchr\"odinger equations with critical exponent and singular electromagneticpotentials. We are concerned with magnetic vector potentials which arehomogeneous of degree -1, including the Aharonov-Bohm class. In particular, byvariational arguments we prove a result of multiplicity of solutionsdistinguished by symmetry properties.

Solutions to nonlinear Schr\"odinger equations with singular electromagnetic potential and critical exponent