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.
|Titolo:||Intertwining semiclassical bound states to a nonlinear magnetic Schrödinger equation|
|Data di pubblicazione:||2009|
|Digital Object Identifier (DOI):||10.1088/0951-7715/22/9/013|
|Appare nelle tipologie:||1.1 Articolo in rivista|