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.
|Titolo:||Multiple solutions to a magnetic nonlinear Choquard equation|
|Data di pubblicazione:||2012|
|Digital Object Identifier (DOI):||10.1007/s00033-011-0166-8|
|Appare nelle tipologie:||1.1 Articolo in rivista|