We consider the stationary nonlinear magnetic Choquard equation, where A is a real-valued vector potential, V is a real-valued scalar potential, N ≥ 3, α ε (0,N)and 2 - (α/N) < p < (2N - α)/(N-2). We assume that both A and V are compatible with the action of some group G of linear isometries of ℝ N. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition u(gx)=τ(g)u(x) for all g ε G, x ε ℝ N, where τ: G → S 1 is a given group homomorphism into the unit complex numbers. © 2011 Springer Basel AG.
Cingolani, S., Clapp, M., Secchi, S. (2012). Multiple solutions to a magnetic nonlinear Choquard equation. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 63(2), 233-248 [10.1007/s00033-011-0166-8].
Multiple solutions to a magnetic nonlinear Choquard equation
SECCHI, SIMONEUltimo
2012
Abstract
We consider the stationary nonlinear magnetic Choquard equation, where A is a real-valued vector potential, V is a real-valued scalar potential, N ≥ 3, α ε (0,N)and 2 - (α/N) < p < (2N - α)/(N-2). We assume that both A and V are compatible with the action of some group G of linear isometries of ℝ N. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition u(gx)=τ(g)u(x) for all g ε G, x ε ℝ N, where τ: G → S 1 is a given group homomorphism into the unit complex numbers. © 2011 Springer Basel AG.
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