We study the existence of ground state standing waves, of prescribed mass, for the nonlinear Schrödinger equation with mixed power nonlinearities i∂tv+Δv+μv|v|q−2+v|v|2javax.xml.bind.JAXBElement@500a707a−2=0,(t,x)∈R×RN, where N≥3, v:R×RN→C, μ>0, 2<2+4/N and 2⁎=2N/(N−2) is the critical Sobolev exponent. We show that all ground states correspond to local minima of the associated Energy functional. Next, despite the fact that the nonlinearity is Sobolev critical, we show that the set of ground states is orbitally stable. Our results settle a question raised by N. Soave [35].
Orbital stability of ground states for a Sobolev critical Schrödinger equation
Visciglia N.
2022-01-01
Abstract
We study the existence of ground state standing waves, of prescribed mass, for the nonlinear Schrödinger equation with mixed power nonlinearities i∂tv+Δv+μv|v|q−2+v|v|2javax.xml.bind.JAXBElement@500a707a−2=0,(t,x)∈R×RN, where N≥3, v:R×RN→C, μ>0, 2<2+4/N and 2⁎=2N/(N−2) is the critical Sobolev exponent. We show that all ground states correspond to local minima of the associated Energy functional. Next, despite the fact that the nonlinearity is Sobolev critical, we show that the set of ground states is orbitally stable. Our results settle a question raised by N. Soave [35].File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.