Abstract
In this paper, we study the existence and concentration of normalized solutions to the nonlinear Schrödinger equation −Δu+k2|x|2u+Ωr2|x|2u−2g|u|2u=2ωu in R2 with ∫R2|u|2dx=1, where ω is the Lagrange multiplier, Ωr is the radial trapping frequency, and g > 0. We show that there is a gk*>0 such that the problem has a ground state solution ug if 0<g<gk* and such a solution does not exist if g≥gk*. Furthermore, we study the limiting behavior of ug when g→gk*.
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