Multiple solutions to nonlinear Schr?dinger equations with singular electromagnetic potential

摘要

We consider the semilinear electromagnetic Schr?dinger equation, where Ω = (?~m{0}) × ?~(N-m) with 2 ≤ m ≤ N, N ≥ 3, 2*: = 2N/(N - 2) is the critical Sobolev exponent, V is a Hardy term and A is a singular magnetic potential of a particular form which includes the Aharonov- Bohm potentials. Under some symmetry assumptions on A we obtain multiplicity of solutions satisfying certain symmetry properties.