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.
Multiple solutions to a magnetic nonlinear Choquard equation / Cingolani, Silvia; Clapp, M.; Secchi, S.. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - 63:2(2012), pp. 233-248. [10.1007/s00033-011-0166-8]
Multiple solutions to a magnetic nonlinear Choquard equation
CINGOLANI, Silvia;
2012-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
