We consider the magnetic NLS equation where N ≥ 3, 2 < p < 2 * 2N/(N - 2), is a magnetic potential and is a bounded electric potential. We consider a group G of orthogonal transformations of , and we assume that A(gx) = gA(x) and V(gx) = V(x) for any g ∈ G, . Given a group homomorphism into the unit complex numbers, we show the existence of semiclassical solutions to problem (0.1), which satisfy for all g ∈ G, . Moreover, we show that there is a combined effect of the symmetries and the electric potential V on the number of solutions of this type.
Intertwining semiclassical bound states to a nonlinear magnetic Schrödinger equation / Cingolani, Silvia; Clapp, M.. - In: NONLINEARITY. - ISSN 0951-7715. - 22:9(2009), pp. 2309-2331. [10.1088/0951-7715/22/9/013]
Intertwining semiclassical bound states to a nonlinear magnetic Schrödinger equation
CINGOLANI, Silvia;
2009-01-01
Abstract
We consider the magnetic NLS equation where N ≥ 3, 2 < p < 2 * 2N/(N - 2), is a magnetic potential and is a bounded electric potential. We consider a group G of orthogonal transformations of , and we assume that A(gx) = gA(x) and V(gx) = V(x) for any g ∈ G, . Given a group homomorphism into the unit complex numbers, we show the existence of semiclassical solutions to problem (0.1), which satisfy for all g ∈ G, . Moreover, we show that there is a combined effect of the symmetries and the electric potential V on the number of solutions of this type.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
