科研之友
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摘要
We study the following nonlinear Schrödinger equationiut=−Δu+V(x)u−a|u|qu,(t,x)∈R1×R2, where a>0, q∈(0,2), and V(x) is some type of trapping potential. For any fixed a>a⁎:=‖Q‖22, where Q is the unique (up to translations) positive radial solution of Δu−u+u3=0 in R2, by directly using constrained variational method and energy estimates we present a detailed analysis of the concentration and symmetry breaking of standing waves for the above equation as q↗2.
