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

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

2010-09-17

arxiv.org/abs/1009.3386v1

Mathematics

Analysis of PDEs

Scientific paper

We investigate existence and qualitative behaviour of solutions to nonlinear Schr\"odinger 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.

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