Multiplicity and concentration of semi-classical solutions to nonlinear Dirac equations
نویسندگان
چکیده
−i~α · ∇w + aβw +M(x)w = f(x, |w|)w for x ∈ R3, where M(x) denotes the scaler field V (x) or V (x)β, and f describes the self-interaction which is either subcritical: W (x)|w|p−2, or critical: W1(x)|w| +W2(x)|w|, with p ∈ (2, 3). We prove multiplicity results with the number of solutions obtained depending on the ratio of minV and lim inf |x|→∞ V (x), as well as maxW and lim sup|x|→∞W (x) for the subcritical case and maxWj and lim sup|x|→∞Wj(x), j = 1, 2, for the critical case. We show also certain concentration phenomenon of the families of semi-classical ground states at saddle points of M(x) = V (x)β.
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